Question 11 Mark
Given that $f ( x )=\left\{\begin{array}{ll}\sqrt{x-1} & x \geq 1 \\ 4 & x<1\end{array}\right.$ Find $f (0)$
Answer
View full question & answer→$f(x)=\sqrt{x-1}, f(x)=4$$f(0)=4$
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Question 21 Mark
Given that $f(x)=\left\{\begin{array}{ll}\sqrt{x-1} & x \geq 1 \\ 4 & x<1\end{array}\right.$ Find $f(3)$
Answer
View full question & answer→$f(x)=\sqrt{x-1}, f(x)=4$</BR>
$f(3)=\sqrt{3-1}$</BR>
$=\sqrt{2}$
$f(3)=\sqrt{3-1}$</BR>
$=\sqrt{2}$
Question 31 Mark
Given that $f ( x )=\left\{\begin{array}{ll}\sqrt{x-1} & x \geq 1 \\ 4 & x<1\end{array}\right.$ Find $f ( a +1)$ in terms of $a$. (Given that $a \geq 0$ )
Answer
View full question & answer→$f(x)=\sqrt{x-1}, f(x)=4$
$f(a+1)=\sqrt{a+1-1}$
$=\sqrt{a}$
$f(a+1)=\sqrt{a+1-1}$
$=\sqrt{a}$
Question 41 Mark
Write the domain of the following real function:
h(x) = x + 6
h(x) = x + 6
Answer
View full question & answer→h(x) = x + 6
The domain is R.
The domain is R.
Question 51 Mark
Write the domain of the following real function:
$f(x)=\frac{2 x+1}{x-9}$
$f(x)=\frac{2 x+1}{x-9}$
Answer
View full question & answer→$f(x)=\frac{2 x+1}{x-9}$The denominator should not be zero as the function is a real function.∴ The domain = R – {9}
Question 61 Mark
Write the domain of the following real function:
$p(x)=\frac{-5}{4 x^2+1}$
$p(x)=\frac{-5}{4 x^2+1}$
Answer
View full question & answer→$p(x)=\frac{-5}{4 x^2+1}$
The domain is R.
The domain is R.
Question 71 Mark
Write the domain of the following real function:
$g(x)=\sqrt{x-2}$
$g(x)=\sqrt{x-2}$
Answer
View full question & answer→$g(x)=\sqrt{x-2}$When x < 2 g(x) becomes complex.But given “g” is real valued functionSo x > 2Domain x ∈ (2, α)
Question 81 Mark
Using the function f and g given below, find fog and gof. Check whether fog = gof
$f(x)=4 x^2-1, g(x)=1+x$
$f(x)=4 x^2-1, g(x)=1+x$
Answer
View full question & answer→$f(x)=4 x^2-1, g(x)=1+x$
$\text { fog }=f[g(x)]$
$=4(1+x)$
$=4(1+x)^2-1$
$=4\left[1+x^2+2 x\right]-1$
$=4+4 x^2+8 x-1$
$=4 x^2+8 x+3$
$\text { gof }=g[f(x)]$
$=g\left(4 x^2-1\right)$
$=1+4 x^2-1$
$=4 x^2$
$\text { fog } \neq g \circ \text { of }$
$\text { fog }=f[g(x)]$
$=4(1+x)$
$=4(1+x)^2-1$
$=4\left[1+x^2+2 x\right]-1$
$=4+4 x^2+8 x-1$
$=4 x^2+8 x+3$
$\text { gof }=g[f(x)]$
$=g\left(4 x^2-1\right)$
$=1+4 x^2-1$
$=4 x^2$
$\text { fog } \neq g \circ \text { of }$
Question 91 Mark
Using the function f and g given below, find fog and gof. Check whether fog = gof
f(x) = 3 + x, g(x) = x – 4
f(x) = 3 + x, g(x) = x – 4
Answer
View full question & answer→f(x) = 3 + x, g(x) = x – 4
fog = f[g(x)]
= f(x – 4)
= 3 + x – 4
= x – 1
gof = g[f(x)]
= g(3 + x)
= 3 + x – 4
= x – 1
fog = gof
fog = f[g(x)]
= f(x – 4)
= 3 + x – 4
= x – 1
gof = g[f(x)]
= g(3 + x)
= 3 + x – 4
= x – 1
fog = gof
Question 101 Mark
Using the function f and g given below, find fog and gof. Check whether fog = gof
$f(x)=x-6, g(x)=x^2$
$f(x)=x-6, g(x)=x^2$
Answer
View full question & answer→$f(x)=x-6, g(x)=x^2$
$f \circ g=f \circ g(x)$
$=f(g(x))$
$\text { fog }=f(x)^2$
$=x^2-6$
$\text { gof }=g \circ f(x)$
$=g(x-6)$
$=(x-6)^2$
$=x^2-12 x+36$
$\text { fog } \neq \text { gof }$
$f \circ g=f \circ g(x)$
$=f(g(x))$
$\text { fog }=f(x)^2$
$=x^2-6$
$\text { gof }=g \circ f(x)$
$=g(x-6)$
$=(x-6)^2$
$=x^2-12 x+36$
$\text { fog } \neq \text { gof }$
Question 111 Mark
Using the function f and g given below, find fog and gof. Check whether fog = gof
$f(x)=\frac{2}{x}, g(x)=2 x^2-1$
$f(x)=\frac{2}{x}, g(x)=2 x^2-1$
Answer
View full question & answer→$f(x)=\frac{2}{x}, g(x)=2 x^2-1$
$f \circ g=f[g(x)]$
$=f\left(2 x^2-1\right)$
$=\frac{2}{2 x^2-1}$
$g \circ f=g[f(x)]$
$=g\left(\frac{2}{x}\right)$
$=2\left(\frac{2}{x}\right)^2-1$
$=2 \times \frac{4}{x^2}-1$
$=\frac{8}{x^2}-1$
$\text { fog } \neq gof$
$f \circ g=f[g(x)]$
$=f\left(2 x^2-1\right)$
$=\frac{2}{2 x^2-1}$
$g \circ f=g[f(x)]$
$=g\left(\frac{2}{x}\right)$
$=2\left(\frac{2}{x}\right)^2-1$
$=2 \times \frac{4}{x^2}-1$
$=\frac{8}{x^2}-1$
$\text { fog } \neq gof$
Question 121 Mark
Using the function f and g given below, find fog and gof. Check whether fog = gof
$f(x)=\frac{x+6}{3}, g(x)=3-x$
$f(x)=\frac{x+6}{3}, g(x)=3-x$
Answer
View full question & answer→$f(x)=\frac{x+6}{3}, g(x)=3-x$
$fog=f[g(x)] $
$=f(3-x) $
$ =\frac{3-x+6}{3}$
$=\frac{9-x}{3} $
$ g \circ f=g[f(x)] $
$ =g\left(\frac{x+6}{3}\right) $
$ =3-\frac{(x+6)}{3}$
$ =\frac{9-x-6}{3} $
$=\frac{3-x}{3} $
$ \text { fog } \neq \text { gof } $
$fog=f[g(x)] $
$=f(3-x) $
$ =\frac{3-x+6}{3}$
$=\frac{9-x}{3} $
$ g \circ f=g[f(x)] $
$ =g\left(\frac{x+6}{3}\right) $
$ =3-\frac{(x+6)}{3}$
$ =\frac{9-x-6}{3} $
$=\frac{3-x}{3} $
$ \text { fog } \neq \text { gof } $
Question 131 Mark
Let $A=\{1,2,3,4\}$ and $B=N$. Let $f: A \rightarrow B$ be defined by $f(x)=x^3$ then, find the range of $f$
Answer
View full question & answer→$A=\{1,2,3,4\}$
$B=\{1,2,3,4,5, \ldots .\}$
$f(x)=x^3$
$f(1)=1^3=1$
$f(2)=2^3=8$
$f(3)=3^3=27$
$f(4)=4^3=64$
$\text { Range }=\{1,8,27,64\}$
$B=\{1,2,3,4,5, \ldots .\}$
$f(x)=x^3$
$f(1)=1^3=1$
$f(2)=2^3=8$
$f(3)=3^3=27$
$f(4)=4^3=64$
$\text { Range }=\{1,8,27,64\}$
Question 141 Mark
Let $A=\{1,2,3,4\}$ and $B=N$. Let $f: A \rightarrow B$ be defined by $f(x)=x^3$ then, identify the type of function
Answer
View full question & answer→$A=\{1,2,3,4\}$
$B=\{1,2,3,4,5, \ldots .\}$
$f(x)=x^3$
$f(1)=1^3=1$
$f(2)=2^3=8$
$f(3)=3^3=27$
$f(4)=4^3=64$
one-one and into function.
$B=\{1,2,3,4,5, \ldots .\}$
$f(x)=x^3$
$f(1)=1^3=1$
$f(2)=2^3=8$
$f(3)=3^3=27$
$f(4)=4^3=64$
one-one and into function.
Question 151 Mark
Determine whether the graph given below represent function. Give reason for your answer concerning graph
Answer
The vertical line cuts the graph at most one point D.
The given graph represents a function.
View full question & answer→The vertical line cuts the graph at most one point D.
The given graph represents a function.
Question 161 Mark
Determine whether the graph given below represent function. Give reason for your answer concerning graph
Answer
The vertical line cuts the graph at A and B.
The given graph does not represent a function.
View full question & answer→The vertical line cuts the graph at A and B.
The given graph does not represent a function.
Question 171 Mark
Determine whether the graph given below represent function. Give reason for your answer concerning graph
Answer
The vertical line cuts the graph at most one point P.
The given graph represent a function.
View full question & answer→ The vertical line cuts the graph at most one point P.
The given graph represent a function.
Question 181 Mark
Determine whether the graph given below represent function. Give reason for your answer concerning graph
Answer
The vertical line cuts the graph at three points S, T, and U.
The given graph does not represent a function.
View full question & answer→The vertical line cuts the graph at three points S, T, and U.
The given graph does not represent a function.
Question 191 Mark
A graph representing the function f(x) is given in it is clear that f(9) = 2
What is the image of 6 under f?
What is the image of 6 under f?
Answer
View full question & answer→The image of 6 under f is 5.
Question 201 Mark
A graph representing the function f(x) is given in it is clear that f(9) = 2
Find the following values of the function
(a) f(0)
(b) f(7)
(c) f(2)
(d) f(10)
Find the following values of the function
(a) f(0)
(b) f(7)
(c) f(2)
(d) f(10)
Answer
View full question & answer→(a) f(0) = 9
(b) f(7) = 6
(c) f(2) = 6
(d) f(10) = 0
(b) f(7) = 6
(c) f(2) = 6
(d) f(10) = 0
Question 211 Mark
A graph representing the function f(x) is given in it is clear that f(9) = 2
For what value of x is f(x) = 1?
For what value of x is f(x) = 1?
Answer
View full question & answer→When f(x) = 1 the value of x is 9.5
Question 221 Mark
A graph representing the function f(x) is given in it is clear that f(9) = 2
Describe the following Domain
Describe the following Domain
Answer
View full question & answer→Domain = {0, 1, 2, 3, …, 10}
= {x / 0 ≤ x ≤ 10, x ∈ R}
= {x / 0 ≤ x ≤ 10, x ∈ R}
Question 231 Mark
A graph representing the function f(x) is given in it is clear that f(9) = 2
Describe the following Range
Describe the following Range
Answer
View full question & answer→Range = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
= {x / 0 ≤ x ≤ 9, x ∈ R}
= {x / 0 ≤ x ≤ 9, x ∈ R}
Question 241 Mark
Given the function $f: x \rightarrow x^2-5 x+6$, evaluate $f(x-1)$
Answer
View full question & answer→Give the function $f : x \rightarrow x ^2-5 x+6$.
$f(x-1)=(x-1)^2-5(x-1)+6$
$=x^2-2 x+1-5 x+5+6$
$=x^2-7 x+12$
$f(x-1)=(x-1)^2-5(x-1)+6$
$=x^2-2 x+1-5 x+5+6$
$=x^2-7 x+12$
Question 251 Mark
Given the function $f : x \rightarrow x ^2-5 x +6$, evaluate $f(-1)$
Answer
View full question & answer→Give the function $f : x \rightarrow x ^2-5 x +6$.
$f(-1)=(-1)^2-5(1)+6$
$=1+5+6$
$=12$
$f(-1)=(-1)^2-5(1)+6$
$=1+5+6$
$=12$
Question 261 Mark
Given the function $f: x \rightarrow x^2-5 x+6$, evaluate $f(2 a)$
Answer
View full question & answer→Give the function $f : x \rightarrow x ^2-5 x+6$.
$f(2 a)=(2 a)^2-5(2 a)+6$
$=4 a^2-10 a+6$
$f(2 a)=(2 a)^2-5(2 a)+6$
$=4 a^2-10 a+6$
Question 271 Mark
Given the function $f: x \rightarrow x^2-5 x+6$, evaluate $f(2)$
Answer
View full question & answer→Give the function f: $x \rightarrow x^2-5 x+6$.
$f(2)=2^2-5(2)+6$
$=4-10+6$
$=0$
$f(2)=2^2-5(2)+6$
$=4-10+6$
$=0$
Question 281 Mark
The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.
| Length ‘x’ of forehand (in cm) | Height 'y' (in inches) |
| 35 | 56 |
| 45 | 65 |
| 50 | 69.5 |
| 55 | 74 |
Check if this relation is a function
Answer
View full question & answer→The relation is y = 0.9 x + 24.5
Yes, the relation is a function.
Yes, the relation is a function.
Question 291 Mark
The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.
| Length ‘x’ of forehand (in cm) | Height 'y' (in inches) |
| 35 | 56 |
| 45 | 65 |
| 50 | 69.5 |
| 55 | 74 |
Find a and b
Answer
View full question & answer→The relation is y = 0.9x + 24.5
When compare with y = ax + b
a = 0.9, b = 24.5
When compare with y = ax + b
a = 0.9, b = 24.5
Question 301 Mark
Let $A=\{1,2,3,7\}$ and $B=\{3,0,-1,7\}$, the following is relation from $A$ to $B$ ?
$R_4=\{(7,-1),(0,3),(3,3),(0,7)\}$
$R_4=\{(7,-1),(0,3),(3,3),(0,7)\}$
Answer
View full question & answer→$A=\{1,2,3,7\} B=\{3,0,-1,7\}$
$A \times B=\{1,2,3\} \times\{3,0,-1,7\}$
$A \times B=\{(1,3)(1,0)(1,-1)(1,7)(2,3)(2,0)(2,-1)(2,7)(3,3)(3,0)(3,-1)(3,7)(7,3)(7,0)(7,-1)(7,7)\}$
$R_4=\{(7,-1),(0,3),(3,3),(0,7)\}$
It is not a relation, there is no element of $(0,3)$ and $(0,7)$ in $A \times B$
$A \times B=\{1,2,3\} \times\{3,0,-1,7\}$
$A \times B=\{(1,3)(1,0)(1,-1)(1,7)(2,3)(2,0)(2,-1)(2,7)(3,3)(3,0)(3,-1)(3,7)(7,3)(7,0)(7,-1)(7,7)\}$
$R_4=\{(7,-1),(0,3),(3,3),(0,7)\}$
It is not a relation, there is no element of $(0,3)$ and $(0,7)$ in $A \times B$
Question 311 Mark
Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?
$R_1$ = {(2, 1), (7, 1)}
$R_1$ = {(2, 1), (7, 1)}
Answer
View full question & answer→A = {1, 2, 3, 7} B = {3, 0, –1, 7}
A × B = {1, 2, 3} × {3, 0, –1, 7}
A × B = {(1, 3) (1, 0) (1, –1) (1, 7) (2, 3) (2, 0) (2, -1) (2, 7) (3, 3) (3, 0) (3, –1) (3, 7) (7, 3) (7, 0) (7, –1) (7, 7)}
$R_1$ = {(2, 1) (7, 1)}
It is not a relation, there is no element of (2, 1) and (7, 1) in A × B
A × B = {1, 2, 3} × {3, 0, –1, 7}
A × B = {(1, 3) (1, 0) (1, –1) (1, 7) (2, 3) (2, 0) (2, -1) (2, 7) (3, 3) (3, 0) (3, –1) (3, 7) (7, 3) (7, 0) (7, –1) (7, 7)}
$R_1$ = {(2, 1) (7, 1)}
It is not a relation, there is no element of (2, 1) and (7, 1) in A × B
Question 321 Mark
Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?
$R_2$ = {(–1, 1)}
$R_2$ = {(–1, 1)}
Answer
View full question & answer→A = {1, 2, 3, 7} B = {3, 0, –1, 7}
A × B = {1, 2, 3} × {3, 0, –1, 7}
A × B = {(1, 3) (1, 0) (1, –1) (1, 7) (2, 3) (2, 0) (2, –1) (2, 7) (3, 3) (3, 0) (3, –1) (3, 7) (7, 3) (7, 0) (7, –1) (7, 7)}
$R_2$ = {(–1, 1)}
It is not a relation, there is no element of (–1, 1) in A × B
A × B = {1, 2, 3} × {3, 0, –1, 7}
A × B = {(1, 3) (1, 0) (1, –1) (1, 7) (2, 3) (2, 0) (2, –1) (2, 7) (3, 3) (3, 0) (3, –1) (3, 7) (7, 3) (7, 0) (7, –1) (7, 7)}
$R_2$ = {(–1, 1)}
It is not a relation, there is no element of (–1, 1) in A × B
Question 331 Mark
Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?
$R_3$ = {(2, –1), (7, 7), (1, 3)}
$R_3$ = {(2, –1), (7, 7), (1, 3)}
Answer
View full question & answer→A = {1, 2, 3, 7} B = {3, 0, –1, 7}
A × B = {1, 2, 3} × {3, 0, –1, 7}
A × B = {(1, 3) (1, 0) (1, –1) (1, 7) (2, 3) (2, 0) (2, –1) (2, 7) (3, 3) (3, 0) (3, –1) (3, 7) (7, 3) (7, 0) (7, –1) (7, 7)}
$R_3$ = {(2, –1), (7, 7), (1, 3)}
Yes, It is a relation
A × B = {1, 2, 3} × {3, 0, –1, 7}
A × B = {(1, 3) (1, 0) (1, –1) (1, 7) (2, 3) (2, 0) (2, –1) (2, 7) (3, 3) (3, 0) (3, –1) (3, 7) (7, 3) (7, 0) (7, –1) (7, 7)}
$R_3$ = {(2, –1), (7, 7), (1, 3)}
Yes, It is a relation
Question 341 Mark
If B × A = {(-2, 3), (-2, 4), (0, 3), (0, 4), (3, 3), (3, 4)} find A and B
Answer
View full question & answer→B × A = {(-2, 3) (-2, 4) (0, 3) (0, 4) (3, 3) (3, 4)}
A = {3, 4}
B = {-2, 0, 3}
A = {3, 4}
B = {-2, 0, 3}