Sample QuestionsFunctions questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The domain of definition of the function $\text{f(x)}=\sqrt{\text{x}-1}+\sqrt{3-\text{x}}$ is :
- A
$[1,\infty)$
- B
$\big(-\infty,3\big)$
- C
$(1,3)$
- ✓
$\big[1,3\big]$
Answer: D.
View full solution →If $\text{x}\neq1$ and $\text{f(x)}=\frac{\text{x}+1}{\text{x}-1}$ is a real function, then $\text{f}(\text{f}(\text{f(2)}))$ is:
Answer: C.
View full solution →The domain of definition of $\text{f(x)}=\sqrt{\frac{\text{x}+3}{(2-\text{x})(\text{x}-5)}}$ is :
- ✓
$(-\infty,-3]\cup(2,5)$
- B
$(-\infty,-3]\cup(2,5)$
- C
$(-\infty,-3]\cup[2,5]$
- D
Answer: A.
View full solution →The range of the function $\text{f(x)}=\frac{\text{x}^2-\text{x}}{\text{x}^2+2\text{x}}$ is :
Answer: C.
View full solution →If $f : R \rightarrow R$ and $g : R \rightarrow R$ are defined by $f(x) = 2x + 3$ and $g(x) = x^2 + 7,$ then the values of $x$ such that $g(f(x)) = 8$ are:
- A
$1, 2$
- B
$-1, 2$
- ✓
$-1, -2$
- D
$1, -2$
Answer: C.
View full solution →Let $\text{f(x)}=\frac{\alpha\text{x}}{\text{x}+1},\text{x}\neq-1.$ Then write the value of $\alpha$ satisfying $\text{f}(\text{f(x)})=\text{x}$ for all $\text{x}\neq-1$
View full solution →If f is a real function satisfying $\text{f}\Big(\text{x}+\frac{1}{\text{x}}\Big)=\text{x}^2+\frac{1}{\text{x}^2}$ for all $\text{x}\in\text{R}-\{0\},$ then write the expression for f(x).
View full solution →Write the domain and range of $\text{f(x)}=\sqrt{\text{x}-[\text{x}]}$
View full solution →Let A and B be two sets such that $n(A) = p$ and $n(B) = q$, write the number of functions from $A$ to $B$.
View full solution →What is the fundamental difference between a relation and a function? Is every relation a function?
Let A = {12, 13, 14, 15, 16, 17} and f : A → Z be a function given by f(x) = highest prime factor of x. Find range of f.
If $\text{f(x)}=\frac{2\text{x}}{1+\text{x}^2},$ show that $\text{f}(\tan\theta)=\sin2\theta$
View full solution →If $f: R \rightarrow R$ be defined by $f(x)=x^2+1$, then find $f^{-1}\{17\}$ and $f^{-1}\{-3\}$
View full solution →Let A = {9, 10, 11, 12, 13} and let f : A → N be defined by f(n) = the highest prime factor of n. Find the range of f.
Find the domain and range of the following real valued functions:
$\text{f(x)}=\frac{\text{ax}+\text{b}}{\text{bx}-\text{a}}$
View full solution →If $\text{f(x)}=\frac{\text{x}-1}{\text{x}+1},$ then show that:
- $\text{f}\Big(\frac{1}{\text{x}}\Big)=-\text{f(x)}$
- $\text{f}\Big(-\frac{1}{\text{x}}\Big)=-\frac{1}{\text{f(x)}}$
View full solution →If $\text{f(x)}=\begin{cases}\text{x}^2,&\text{when }\text{ x}<0\\\text{x},&\text{when }\ 0\leq\text{x}<1\\\frac{1}{\text{x}},&\text{when }\text{ x}>0\end{cases}$
Find:
- $\text{f}\Big(\frac{1}{2}\Big)$
- $\text{f}(-2)$
- $\text{f}(1)$
- $\text{f}(\sqrt{3})$
- $\text{f}(\sqrt{-3})$
View full solution →If $\text{y}=\text{f(x)}=\frac{\text{ax}-\text{b}}{\text{bx}-\text{a}},$ show that x = f(y).
View full solution →If $\text{f(x)}=\log_\text{e}(1-\text{x})$ and $\text{g(x)}=[\text{x}],$ then determine the following functions:
(fg)(0)
View full solution →Find $\text{f}+\text{g},\text{ f}-\text{g},\text{ cf}(\text{c}\in\text{ R},\text{c}\neq0),\text{ fg},\frac{1}{\text{f}}$ and $\frac{\text{f}}{\text{g}}$ in the following:
If $f(x) = x^3 + 1$ and $g(x) = x + 1$
View full solution →Let f and g be two real functions defined by $\text{f(x)}=\sqrt{\text{x}+1}$ and $\text{g(x)}=\sqrt{9-\text{x}^2}$ Then describe the following functions:
g - f
View full solution →Let f and g be two real functions defined by $\text{f(x)}=\sqrt{\text{x}+1}$ and $\text{g(x)}=\sqrt{9-\text{x}^2}$ Then describe the following functions:
$\text{f}^2+7\text{f}$
View full solution →If $\text{f(x)}=\log_\text{e}(1-\text{x})$ and $\text{g(x)}=[\text{x}],$ then determine the following functions:
(f + g)(-1)
View full solution →Let $f(x) = x^2 $ and $g(x) = 2x + 1$ be two real functions. Find $(f + g)(x), (f - g)(x), (fg)(x)$ and $\Big(\frac{\text{f}}{\text{g}}\Big)\text{x}$
View full solution →Let f and g be two real functions defined by $\text{f(x)}=\sqrt{\text{x}+1}$ and $\text{g(x)}=\sqrt{9-\text{x}^2}$ Then describe the following functions:
$\frac{5}{\text{g}}$
View full solution →If for non-zerox, $\text{af(x)}+\text{bf}\Big(\frac{1}{\text{x}}\Big)=\frac{1}{\text{x}}-5,$ where $\text{a}\neq\text{b},$ then find f(x).
View full solution →Let $\text{f}:[0,\infty)\rightarrow\text{R}$ and $\text{g}:\text{R}\rightarrow\text{R}$ be defined by $\text{f(x)}=\sqrt{\text{x}}$ and g(x) = x. Find f + g, g - g, fg and $\frac{\text{f}}{\text{g}}$
View full solution →Let f and g be two real functions defined by $\text{f(x)}=\sqrt{\text{x}+1}$ and $\text{g(x)}=\sqrt{9-\text{x}^2}$ Then describe the following functions:
$\frac{\text{g}}{\text{f}}$
View full solution →Let f and g be two real functions defined by $\text{f(x)}=\sqrt{\text{x}+1}$ and $\text{g(x)}=\sqrt{9-\text{x}^2}$ Then describe the following functions:
$2\text{f}-\sqrt{5}\text{g}$
View full solution →If $\text{f(x)}=\log_\text{e}(1-\text{x})$ and $\text{g(x)}=[\text{x}],$ then determine the following functions:
$\frac{\text{f}}{8}$
View full solution →