Sample QuestionsDomain and Range of Functions questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Let $f$ and $g$ be real function be $f(x)=\sqrt{x+4}, x \geq-4$ and $g(x)=\sqrt{x-4}, x \geq 4$. Then function $f g$ is
- ✓
$\sqrt{x^2-16}$
- B
$\sqrt{x^2-4}$
- C
$\sqrt{x^2+1}$
- D
$\sqrt{x^2-1}$
Answer: A.
View full solution →The domain and range of the function $f$ given by $f(x)=2-|x-5|$ is
- A
Domain $=R^{+}$, Range $=(-\infty, 1]$
- ✓
Domain $=R$, Range $=(-\infty, 2]$
- C
Domain $=R$, Range $=(-\infty, 2)$
- D
Domain $=R^{+}$, Range $=(-\infty, 2]$
Answer: B.
View full solution →If $[x]^2-5[x]+6=0$, where $[$.$] denote the greatest$ integer function, then
- A
$x \in[3,4]$
- B
$x \in(2,3]$
- ✓
$x \in[2,3]$
- D
$x \in[2,4)$
Answer: C.
View full solution →Let $f(x)=\sqrt{1+x^2}$, then
Answer: C.
View full solution →Domain of $\sqrt{a^2-x^2}(a>0)$ is
- A
$(-a, a)$
- ✓
$[-a, a]$
- C
$[0, a]$
- D
$(-a, 0]$
Answer: B.
View full solution →Draw the graph of constant function $f: R \rightarrow R ; f(x)$ $=2 \forall x \in R$. Also, find its domain and range.
View full solution →Find the range of the function $f(x)=1-|x-2|$
View full solution →Find the domain of the function $f(x)=\frac{1}{\log (4-x)}$.
View full solution →Find the range of the function $f(x)=\sqrt{x^2+4}$.
View full solution →Let $f$ be the subset of $Z \times Z$ defined by $f=\{(a b, a+b): a, b \in Z\}$. Is $f$ a function from $Z$ to Z ? Justify your answer.
View full solution →Find the domain and range of the real functions$
f(x)=\frac{|x-1|}{x-1}
$
View full solution →Find the domain of the function
$
f(x)=\frac{1}{\sqrt{[x]^2-[x]-6}}
$
View full solution →If $f(x)=y=\frac{a x-b}{c x-a}$, then prove that $f(y)=x$.
View full solution →Let $f$ and $g$ be real functions defined by
$
f(x)=2 x+1 \text { and } g(x)=4 x-7
$
(a) For what real numbers $x, f(x)=g(x)$ ?
(b) For what real numbers $x, f(x)<g(x)$ ?
View full solution →Draw the graph of the function $|x-2|$.
View full solution →Draw the graph of the function
$
f(x)=\left\{\begin{array}{ll}
1+2 x, & x<0 \\
3+5 x, & x \geq 0
\end{array}\right.
$
Also, find its range.
View full solution →Draw the graph of following function and find range $\left(R_f\right)$ of $f(x)=|x-2|+|2-x| \forall-3 \leq x \leq 3$. U
View full solution →Find the domain and range of the following functions:
(i) $f(x)=\frac{1}{\sqrt{x-5}}$
(ii) $f(x)=\left\{\left(\frac{x^2-1}{x-1}\right): x \in R, x \neq 1\right\}$
View full solution →Let $A=\{9,10,11,12,13\}$ and let $f: A \rightarrow N$ defined by $f(n)=$ the highest prime factor of $n$. Find the range of $f$.
View full solution →If $f: R \rightarrow R$ is defined by $f(x)=3 x+2$, then value of $f[f(x)]$ is _________________
View full solution →The range of the function $f(x)=|x-3|$ is _________________.
View full solution →The domain of $f(x)=x|x|$ is _________________.
View full solution →If $f$ and $g$ are two real valued functions defined as $f(x)=2 x+1, g(x)=x^2+1$, then $f g$ _________________
View full solution →If $f(x)=x^3$, then the value of $\frac{f(5)-f(1)}{5-1}$ is _________________
View full solution →Find the domain and range of $f(x)=|2 x-3|-3$.
View full solution →Draw the graph of the function
$
f(x)=\left\{\begin{array}{ll}
\frac{|x|}{x}, & x \neq 0 \\
0 . & x=0
\end{array}\right.
$
View full solution →If $f(x)=\frac{4 x+3}{6 x-4}, x \neq \frac{2}{3}$, then show that $(f o f)(x)=x$ for all $x \neq \frac{2}{3}$. What is the inverse of $f$.
View full solution →Redefine the function $
f(x)=|x-2|+|2+x|,-3 \leq x \leq 3
$
View full solution →Find the domain of function$
f(x)=\sqrt{4-x}+\frac{1}{\sqrt{x^2-1}}
$
View full solution →If the function $f: R \rightarrow R$ be given by $f(x)=x^2+2$ and $g: R \rightarrow R$ be given by $g(x)=\frac{x}{x-1}, x \neq 1$, then match the following :| (a) $f o g(2)$ | (i) 38 |
| (b) $g o f(2)$ | (ii) 2 |
| (c) $f o f(2)$ | (iii) 6 |
| (d) $g o g(2)$ | (iv) $\frac{6}{5}$ |
View full solution →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 :| (a) $f-g$ | (i) $\left\{\left(2, \frac{4}{5}\right),\left(8,-\frac{1}{4}\right),\left(10, \frac{-3}{13}\right)\right\}$ |
| (b) $f+g$ | (ii) $\{(2,20),(8,-4),(10,-39)\}$ |
| (c) $f.g$ | (iii) $\{(2,-1),(8,-5),(10,-16)\}$ |
| (d) $\frac{f}{g}$ | (iv) $\{(2,9),(8,3),(10,10)\}$ |
View full solution →