Sample QuestionsFunction questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Which of the following is a sufficient condition for two different functions to be equal ?
- A
Domains of both the functions must be same
- B
Ranges of both the functions must be same
- ✓
$(a)$ and $(b)$
- D
$(a)$ or $(b)$
Answer: C.
View full solution →What is the type of function $f: Z-\{0\} \rightarrow N$ and $f(x)=x^2, x \in Z-\{0\} ?$
Answer: B.
View full solution →Which of the following statements is true for one - one function ?
- A
Only for two values of the domain, their images should be different.
- B
For any two values of the domain, their images are same.
- ✓
For any two different values of the domain. their images are different.
- D
For each value of the domain, their images are same.
Answer: C.
View full solution →What is the type of function $f: A \rightarrow B$, where each value of domain $A$ has the same image in set $B?$
Answer: C.
View full solution →What is the type of function f :$ A \rightarrow B,$ wherein, for two different values of domain their functional values are same ?
Answer: B.
View full solution →$F:$ $N \rightarrow N, f(t)=t^2+1, t \in N$. Determine the type of function $f$.
View full solution →$f: Z \rightarrow N, f(t)=t^2+1, t \in Z$. Determ the type of function $f$.
View full solution →$f:\{1,2,3\} \quad N, g:\{2,3,4\} \quad N, f(x)=2 x+1$ and $g(x)=x-1$. Can these two functions $f$ and $g$ be equal functions? Why ?
View full solution →Define constant function in notations.
Define many-one function in notations.
$f: \mathrm{A} \rightarrow \mathrm{B}, f(x)=1-4 x$ and $g: \mathrm{A} \rightarrow \mathrm{C}, g(x)=6 x+1$ and $\mathrm{A}=\{0,1,2\} .$ Are $f$ and $g$ equal functions ?
View full solution →$f: \mathrm{A} \rightarrow \mathrm{B}, \mathrm{A}=\{1,3\}, \mathrm{B}=\{1,4,9,16\}, f(x)=x^{2}$ and $g: \mathrm{A} \rightarrow \mathrm{B}, \mathrm{A}=\{1,3\}$, $\mathrm{B}=\{1,4,7,9,11\} g(x)=4 x-3 .$ Check the equality of the functions $f$ and $g .$
View full solution →If $f=\mathbf{N} \rightarrow \mathbf{N}, f(x)=x^{2}$ and $g=\mathbf{Z}-\{0\} \rightarrow \mathbf{N}, g(x)=x^{2}$, can we say that $f$ and $g$ are equal functions ?
View full solution →$(i) f: Z \rightarrow R$ and $f(x)=100$ then state the type of function $f$.
$(ii)$ State the type of the function between dates of a month and days of the week.
View full solution →$f: \mathrm{Z} \rightarrow \mathbf{N} \cup\{0\}, f(x)=x^{2}$ then state the type of function $f$.
View full solution →Find domain, co-domain and range for the following functions :
$(1)$ $f: \mathrm{A} \rightarrow \mathrm{N}, f(x)=x^{2}+1, \mathrm{~A}=\{x \mathrm{I}-2 \leq x<1, x \in \mathrm{Z}\}$
$(2)$ $f: \mathrm{Z} \rightarrow \mathrm{N}, f(x)=x^{2}+2, x \in \mathrm{Z}$
$(3)$ $f: \mathrm{N} \rightarrow \mathrm{N}, f(x)=4 x, x \in \mathrm{N}$
View full solution →If $f(x)=x^{2}-4 x+8$ then for which value of $x$, is $f(2 x)=2 f(x) ?$
View full solution →$f(x)=x(2 x-7)$ where $x \in$ R. If $f(x)=15$ then find the value of $x$.
View full solution →If $f(x)=x^{3}+3^{x}-x^{2}-2^{x}$ then find $f(3)-6 f(2)$
View full solution →If $f(x) \frac{x^{3}+1}{x^{2}-2 x+1}$ where $x \in \mathbf{Z}-\{1\}$ then find $f(-2), f(-1)$ and $f(0)$.
View full solution →Obtain domain, co-domain and range for the following functions :
$(1)$ $f: \mathrm{A} \rightarrow \mathrm{B}, \mathrm{A}=\{-1,0,1\}, \mathrm{B}=\{1,2,3,4,5,6,7\}, f(x)=2 x+5, x \in \mathrm{A}$
$(2)$ $g: \mathrm{A} \rightarrow \mathrm{N}, \mathrm{A}=\{-1,2,3,4\}, g(x)=3 x+5, x \in \mathrm{A}$
$(3)$ $h: \mathrm{P} \rightarrow \mathrm{S}, \mathrm{P}=\{-2,-1,0,1\}, \mathrm{S}=\{-4,-3,-2,-1\}, h(x)=x-2, x \in \mathrm{P}$
$(4)$ $k: \mathrm{A} \rightarrow \mathrm{Z}, \mathrm{A}=\left\{-\frac{1}{2}, 0, \frac{1}{2}\right\}, k(\mathrm{x})=4 x^{2}+3, x \in \mathrm{A}$
View full solution →Verify whether relations between the elements of the sets given below are
functions or not.
(1) $\mathrm{A}=\{1,2,3,4\}, \mathrm{B}=\{3,5,7,9\}$, and relation is $f(x)=2 x+1, x \in \mathrm{A}$
(2) $\mathrm{P}=\left\{-\frac{1}{2}, 0,1\right\}, \mathrm{S}=\{10\}$, and rule is $k(x)=10, x \in \mathrm{P}$
(3) $\mathrm{A}=\{2,5,6\}, \mathrm{B}=\left\{1, \frac{3}{2}, \frac{9}{5}, \frac{11}{7}, \frac{13}{6}\right\}$, and rule is $y=\frac{2 x-1}{x+1}, x \in \mathrm{A}$
(4) $\mathrm{B}=\{-1,0,1,3\}, \mathrm{C}=\{-5,-3,-1,1,3\}$, and rule is $h(x)=2 x+3, x \in \mathrm{B}$
View full solution →If $g(x)=\sqrt{36-x^{2}},-6 \leq x \leq 6 ;$ find $g(0), g(-3), g$ $(5), g(-6)$ and $g(2) .$
View full solution →If $\mathrm{f}: R \rightarrow R$ and $\mathrm{f}(\mathrm{x})=5 x^{2}-7 x+9$, find $\mathrm{f}(0)$, $\mathrm{f}(1), \mathrm{f}(-2)$ and $f\left(\frac{1}{2}\right) .$
View full solution →