Question 11 Mark
$F:$ $N \rightarrow N, f(t)=t^2+1, t \in N$. Determine the type of function $f$.
Answer$f: N \rightarrow N . \therefore N=\{1,23,4, . .\} \text { and } N=\{1,2,3,4, \ldots\}$
$f(1)=t^2+1, t \in N$
$f(1)=1+1=2$
$f(2)=2^2+1=5$
Here, for two different elements of do - main A , their images are different in co - domain. Therefore, function $f$ is one - one function.
View full question & answer→Question 21 Mark
$f: Z \rightarrow N, f(t)=t^2+1, t \in Z$. Determ the type of function $f$.
Answer$f : Z \rightarrow N$.
$\therefore Z=\{\ldots-3,-2,-1,0,1,2,3, \ldots\}$ and $N=\{1,2,3,4, \ldots\}$
$f(t)=t^2+1, t \in Z$
$\therefore f(-3)=9+1=10, f(3)=9+1=10, f(-2)=4+1=5 f(2)=4+1=5$
Here, for two different elements of domain A, their images are same in co-domain. Therefore, function / is many-one function.
View full question & answer→Question 31 Mark
$f:\{1,2,3\} \quad N, g:\{2,3,4\} \quad N, f(x)=2 x+1$ and $g(x)=x-1$. Can these two functions $f$ and $g$ be equal functions? Why ?
Answer$f :\{1,2,3\} \rightarrow N$ and $g :\{2,3,4\} \rightarrow 1$. Domain of $f$ and g are not equal.
Therefore, $f$ and g are not equal functions.
View full question & answer→Question 41 Mark
Define constant function in notations.
AnswerSuppose, $f: A \rightarrow B$. If for each element $x_1, x_2, x_3, \ldots .$. Of domain. the image is same in co - domain $B$, i.e., $f\left(x_1\right)=f\left(x_2\right)=$ $\left(f\left(x_3\right)=\ldots\right.$ then, function $f$ is called constant function.
View full question & answer→Question 51 Mark
Define many-one function in notations.
AnswerSuppose. $f: A \rightarrow B$. If for any two differents $x_1, x_2$ of domain $A$. $f\left(x_1\right)=f\left(x_2\right)$.
Then function $f$ is called many-one function.
View full question & answer→Question 61 Mark
Define one-one function in notations.
AnswerSuppose. $f: A \rightarrow B$. If for any two different elements $x_1$ and $X_2 \cdot f\left(x_1\right) \neq f\left(x_2\right)$ then function $f$ is called one-one function.
View full question & answer→Question 71 Mark
$g : N \rightarrow N$, 'subtract $2$ from the elements of the domain'. Can this rule be called a function?
Answer$g:$ $N \rightarrow N$, i.e., $N=\{1,2,3, \ldots\} ; N=\{1,2,3, \ldots\}$. Therefore, 'subtract $2$ from the elements of the domain' this rule cannot be called a function.
View full question & answer→Question 81 Mark
$f: A \rightarrow B, A=\{-3,-1,1,3\} ;$
$B=\{1,0,9\}: f(x)=x^2 . \text { Is } f$ a function?
Answer$f: A \rightarrow B, A=\{-3,-1,1,3\} ; B=\{1,0,9\} ; f(x)=x^2$. Therefore, $f$ is a function.
View full question & answer→Question 91 Mark
Define a function of real variable.
AnswerIf $f: A \rightarrow B$. Where $A \subset R$ then $f$ is called a function of real variable.
View full question & answer→Question 101 Mark
Give the necessary condition for defining a function.
AnswerThe necessary condition for defining a function is that ‘domain and co-domain of the function should not be empty sets.’
View full question & answer→Question 111 Mark
If $\mathrm{f}(\mathrm{x})=\frac{1}{2 x}+\frac{1}{x-3}$ then find $f(2) f\left(\frac{1}{2}\right)$.
View full question & answer→Question 121 Mark
State the type of following functions : $g: R \rightarrow$ $R, g(x)=7, x \in R$
View full question & answer→Question 131 Mark
State the type of following functions: $f: N \rightarrow$ $Z, f(x)=x^{2}-4 x, x \in N$
View full question & answer→Question 141 Mark
Determine type of the following functions: $f: N \rightarrow$ $N, f(x)=8, x \in N$
View full question & answer→Question 151 Mark
Determine type of the following functions: $h: N \rightarrow$ $Z, h(x)=5 x-x^{2}, x \in N$
View full question & answer→Question 161 Mark
Determine type of the following functions: $g: R \rightarrow$ $R, g(x)=x^{2}+2 x-8, x \in R$
View full question & answer→Question 171 Mark
Determine type of the following functions: $f: N \rightarrow$ $N, f(x)=x^{2}+x+1, X \in N$
View full question & answer→Question 181 Mark
Determine type of the following functions: $f: Z-\{5\} \rightarrow$ $R, f(x)=\frac{x^{2}-9 x+20}{x 5}$
View full question & answer→Question 191 Mark
Determine type of the following functions: $f: N \rightarrow$$Z, f(x)=3 x-5, x \in N$
View full question & answer→Question 201 Mark
For $\mathrm{f}: A \rightarrow B, A \subset R-\{0\}, \mathrm{B}=\mathrm{R}$ and $f(x)=\frac{1}{x}$, then is $\mathrm{f}$ a function?
AnswerFor $\mathrm{f}: A \rightarrow B, A \subset R-\{0\}, \mathrm{B}=\mathrm{R}$ and $f(x)=\frac{1}{x}$then, $\mathrm{f}$ is a function.
View full question & answer→Question 211 Mark
What is the function whose range is singleton set?
AnswerThe function whose range is singleton set is constant function.
View full question & answer→Question 221 Mark
If $g(x)=5 x+11$ and $x=\{-1,0,1\}$, find the range of the function.
Answer$R_{g}=\{g(-1), g(0), g(1)\}=\{6,11,16\}$
View full question & answer→Question 231 Mark
If $\mathrm{f}: R \rightarrow R$ and $\mathrm{f}(\mathrm{x})=3 x^{2}+5$, state the type of the function.
AnswerIf $\mathrm{f}: R \rightarrow R$ and $\mathrm{f}(\mathrm{x})=3 x^{2}+5$, then it is a real function.
View full question & answer→Question 241 Mark
Write the range of the function in symbol.
AnswerFor $\mathrm{f}: A \rightarrow B$
range $R_{f}=f(A)=\{f(x) \mid x \in A\}$
For every $f(x) \in f(A) \cdot f(x) \in B$.
Hence, $f(A) \subset B \rightarrow R_{f} \subset B$.
View full question & answer→Question 251 Mark
AnswerIf the domain and range both defined on real number set R, then it is called real function.
View full question & answer→Question 261 Mark
AnswerThe functions defined on same domain and for each element of the domain their images are same, then such two functions are called equal functions.
View full question & answer→Question 271 Mark
Define a constant function.
AnswerIf for each element of domain of a function the image or functional value is same then function is called a constant function.
View full question & answer→Question 281 Mark
What is called the unique relation between the elements of two non-empty sets?
AnswerThe unique relation between the elements of two non-empty sets is called a function.
View full question & answer→Question 291 Mark
If $f: R \rightarrow N ; f(x)=3$, what is the range of the function?
AnswerFor every $x \in R, \mathrm{f}(\mathrm{x})=3$. Hence the range of $\mathrm{f}$ is $\{3\}$.
View full question & answer→Question 301 Mark
What is called f (x) in function?
AnswerIn the function f (x) is called the reflection of x at f or the value of x at f
View full question & answer→Question 311 Mark
How does the function associate its domain and co-domain?
AnswerThe function associates each element of its domain to the unique element of its co-domain.
View full question & answer→Question 321 Mark
Are the various type of relations between the elements of set $A$ and the elements of set $B$ function?
AnswerThe various type of all the relations between the elements of set $A$ and the elements of set $B$ are not the function.
View full question & answer→Question 331 Mark
If for $\mathrm{f}: A \rightarrow B$, we get $y \in B$, corresponding to $x \in A$, then how is lt denoted by symbol?
AnswerIf for $\mathrm{f}: A \rightarrow B$, we get $y \in B$ corresponding to $x \in$ $A$, then it is denoted by symbol as $\mathrm{y}=\mathrm{f}(\mathrm{x})$.
View full question & answer→Question 341 Mark
If $\mathrm{f}: A \rightarrow B$, by which symbol is the element $\mathrm{x}$ of $\mathrm{A}$ shown by the relation $\mathrm{f}$ ?
AnswerIf $\mathrm{f}: A \rightarrow B$, the element $\mathrm{x}$ of $\mathrm{A}$ is shown in symbol by $\mathrm{f}(\mathrm{x})$.
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