Sample QuestionsRelations and Functions questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $f(x) = ax + b$, where a and b are integers, $f(–1) = –5$ and $f(3) = 3,$ then $a$ and $b$ are equal to.
- A
$a = –3, b = –1$
- ✓
$a = 2, b = –3$
- C
$a = 0, b = 2$
- D
$a = 2, b = 3$
Answer: B.
View full solution →The domain and range of real function $f$ defined by $\text{f(x)}=\sqrt{\text{x}-1}$ is given by.
- ✓
Domain $= [1, \infty),$ Range $= [0, \infty)$
- B
Domain $= [1, \infty),$ Range $= [0, \infty)$
- C
Domain $= [1, \infty),$ Range $= [0, \infty)$
- D
Domain $= [1, \infty),$ Range $= [0, \infty)$
Answer: A.
View full solution →The domain of the function $f$ defined by $\text{f(x)}=\sqrt{4-\text{x}}+\frac{1}{\sqrt{\text{x}^2-1}}$ is equal to.
- ✓
$(–\infty, –1) \cup (1, 4]$
- B
$(–\infty, –1] \cup (1, 4]$
- C
$(–\infty, –1) \cup [1, 4]$
- D
$(–\infty, –1) \cup [1, 4)$
Answer: A.
View full solution →Domain of $\sqrt{\text{a}^2-\text{x}^2}(\text{a}>0)$ is.
- A
$(-a, a)$
- ✓
$[-a, a]$
- C
$[0, a]$
- D
$(-a, 0]$
Answer: B.
View full solution →The domain of the function $f$ given by $\text{f(x)}=\frac{\text{x}^2+2\text{x}+1}{\text{x}^2-\text{x}-6}.$
- ✓
$R – \{3, –2\}$
- B
$R – \{–3, 2\}$
- C
$R – [3, –2]$
- D
$R – (3, –2)$
Answer: A.
View full solution →If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, then $(\text{A} × \text{B})\cup (\text{A} × \text{C})$
= {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}.
View full solution →If $(\text{x}-2, \text{y}+5)=\big(-2, \frac{1}{3}\big)$ are two equal ordered pairs, then $\text{x}=4, \text{y}=\frac{-14}{3}.$
View full solution →If A × B = {(a, x), (a, y), (b, x), (b, y)}, then A = {a, b}, B = {x, y}
If P = {1, 2}, then P × P × P = {(1, 1, 1), (2, 2, 2), (1, 2, 2), (2, 1, 1)}
The ordered pair (5, 2) belongs to the relation $\text{R}=\{(\text{x, y}):\text{y = x}-5, \text{x, y}\in\text{Z}\}$
View full solution →Let A = {–1, 2, 3} and B = {1, 3}. Determine:
B × A
If f and g are real function defined by$ f(x) = x^2 + 7$ and $g(x) = 3x + 5,$ find following $: f(3) + g (– 5)$
View full solution →Find the domain of each of the following functions given by:
$\text{f(x)}=\frac{3\text{x}}{28-\text{x}}$
View full solution →Let $\text{f(x)}=\sqrt{\text{x}}$ and $\text{g(x)}=\text{x}$ be two functions defined in the domain $\text{R}^+\cup\{0\}$. Find:
$\text{(fg)(x)}$
View full solution →Is the given relation a function? Give reasons for your answe $r:s = (n, n^{2 }) | n$ is a positive integer
View full solution →In following case, find a and b.
$\big(\frac{\text{a}}{4}, \text{a}-2\text{b}\big)=(0, 6+\text{b})$
View full solution →Find the domain of function given by $: \text{f}\text{(x)}=\frac{1}{\sqrt{\text{x}+|\text{x}|}}$
View full solution →Find the domain of following function given by $: \text{f(x)}=\frac{\text{x}^3-\text{x}+3}{\text{x}^2-1}$
View full solution →If $f$ and $g$ are real function defined by $f(x) = x^2 + 7$ and $g(x) = 3x + 5,$ find following:
$f(-2) + g(-1)$
View full solution →Let f and g be real functions defined by f(x) = 2x + 1 and g(x) = 4x - 7.
For what real numbers x, f(x) < g(x)?
If $\text{f(x)}=\text{y}=\frac{\text{ax}-\text{b}}{\text{cx}-\text{a}}$ then prove that f(y) = x.
View full solution →Find the values of $x$ for which the functions:
$f(x) = 3x^2 – 1$ and $g(x) = 3 + x$ are equal.
View full solution →Find the domain and Range of the function $\text{f(x)}=\frac{1}{\sqrt{\text{x}-5}}.$
View full solution →Express the following functions as set of ordered pairs and determine their range. $f : X \rightarrow R, f(x) = x^3 + 1,$ where $X = {–1, 0, 3, 9, 7}$
View full solution →If$\text{A}= \big\{\text{x} : \text{x}\in\text{W}, \text{x}\in2\big\},$$\text{B}= \big\{\text{x} : \text{x}\in\text{N},1< \text{x} < 5\big\},$$\text{C}=\big\{3, 5\big\}$ find. - $\text{A}\times(\text{B} \cap \text{C}) $
- $\text{A}\times(\text{B} \cup \text{C}) $
View full solution →Let f and g be two real functions given by
f = {(0, 1), (2, 0), (3, – 4), (4, 2), (5, 1)}
g = {(1, 0), (2, 2), (3, – 1), (4, 4), (5, 3)}
Then the domain of f.g is given by _________.
Let f = {(2, 4), (5, 6), (8, – 1), (10, – 3)}
g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, 5)}
be two real functions. Then Match the following:
| Column I | Column II |
| (a) | $\text{f}-\text{g}$ | (i) | $\Big\{\Big(2, \frac{4}{5}\Big), \Big(8, \frac{-1}{4}\Big), \Big(10, \frac{-3}{13}\Big)\Big\}$ |
| (b) | $\text{f}+\text{g}$ | (ii) | $\{(2, 20), (8, -4), (10, -39)\}$ |
| (c) | $\text{f}\times\text{g}$ | (iii) | $\{(2, 1), (8, -5), (10, -16)\}$ |
| (d) | $\frac{\text{f}}{\text{g}}$ | (iv) | $\{(2, 9), (8, 3), (10, 10)\}$ |
View full solution →Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? Justify. If this is described by the relation, $\text{g(x)} = \alpha\text{x} + \beta,$ then what values should be assigned to $\alpha$ and $\beta?$
View full solution →