Functions PYQs - Last 5 Years

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Practice 58 TS EAMCET Mathematics questions from Functions. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 5 Years Functions Questions

Showing 50 of 58 filtered questions.

If $\frac{x+1}{x^3(x-1)}=\frac{a}{x}+\frac{b}{x^2}+\frac{c}{x^3}+\frac{d}{x-1}$, then

The domain of the real valued function $f(x)=\log _{\sqrt{2}}\left(\sqrt{x^2+x}+\sqrt{x^2-x}\right)$ is

The domain and range of $f(x)=\frac{1}{\sqrt{|x|-x^2}}$ are $A$ and $B$ respectively. Then $A \cup B=$

A function $f: R \rightarrow R$ defined by
$$ f(x)=\left\{\begin{array}{c} 2 x+3, x \leq \frac{4}{3} \\ -3 x^2+8 x, x>\frac{4}{3} \end{array}\right. \text { is } $$

Consider the following statements
Statement $\mathrm{I} \cosh ^{-1} x=\tanh ^{-1} x$ has no solution
Statement II $\cosh ^{-1} x=\operatorname{coth}^{-1} x$ has only one solution
The correct answer is

If $2^{4 n+3}+3^{3 n+1}$ is divisible by $P$ for all natural numbers $n$, then $P$ is

If the domain of the real valued function $f(x)=\frac{1}{\sqrt{\log _{\frac{1}{3}}\left(\frac{x-1}{2-x}\right)}}$ is $(a, b)$, then $2 b=$

A real valued function $f:[4, \infty) \rightarrow R$ is defined as $f(x)=\left(x^2+x+1\right)^{\left(x^2-3 x-4\right)}$, then $f$ is

If $D \subseteq R$ and $f: D \rightarrow R$ defined by $f(x)=\frac{x^2+x+a}{x^2-x+a}$ is a surjection, then ' $a$ ' lies in the interval.

If the range of the real valued function $f(x)=\frac{x^2+x+k}{x^2-x+k}$ is $\left[\frac{1}{3}, 3\right]$, then $k=$

For a real number ' $a$ ', if a real valued function $f(x)=4 x^3+a x^2+3 x-2$ is monotonic in its domain, then the range of ' $a$ ' is

Let $f: R \rightarrow R$ be defined by $f(x)=5^{-|x|}+\operatorname{sgn}\left(5^{-x}\right)$, where sgn $x$ denotes signum function of $x$. Then $f$ is

If $\frac{x^3+3}{(x-3)^3}=a+\frac{b}{x-3}+\frac{c}{(x-3)^2}+\frac{d}{(x-3)^3}$, then $(a+d)-(b+c)=$

If $f(x)=\tan \left(\frac{\pi}{\sqrt{x+1}+4}\right)$ is a real valued function, then the range of $f$ is

The inverse of the function $y=\frac{10^x-10^{-x}}{10^x+10^{-x}}+1$ is $x=$

If $f: R-\{0\} \rightarrow R$ is defined by $3 f(x)+4 f\left(\frac{1}{x}\right)=\frac{2-x}{x}$ then $f(3)=$

The domain of the real valued function $f(x)=\sqrt{\cos (\sin x)}+\cos ^{-1}\left(\frac{1+x^2}{2 x}\right)$ is

If $f(x)=\frac{2 x-3}{3 x-2}$ and $f_n(x)=($ fofofo .......n times) $(x)$, then $f_{32}(x)=$

$f$ is a real valued function satisfying the relation $f\left(3 x+\frac{1}{2 x}\right)=9 x^2+\frac{1}{4 x^2}$. If $f\left(x+\frac{1}{x}\right)=1$, then $x$ is equal to

The domain of the real valued function $f(x)=\sqrt[3]{\frac{x-2}{2 x^2-7 x+5}}+\log \left(x^2-x-2\right)$ is

$f(x)=a x^{2}+b x+c$ is an even function and$g(x)=p x^{3}+q x^{2}+r x$ is an odd function.If $h(x)=f(x)+g(x)$ and $h(-2)=0$, then $8 p+4 q+2 r=$

If $f$ is a real valued function from $A$ onto $B$ defined by $f(x)=\frac{1}{\sqrt{|x-|x||}}$, then $A \cap B=$

The range of the real valued function $f(x)=\log _{3}\left(5+4 x-x^{2}\right)$ is

The sum of the maximum and minimum values of the function $f(x)=\frac{x^{2}-x+1}{x^{2}+x+1}$ is

Let $X=\left\{\left.\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] \right\rvert\, a, b, c, d \in R\right\}$. If $f: X \rightarrow R$ is defined by $f(A)=\operatorname{det}(A) . \forall A \in X$, then $f$ is

If ${ }^n C_r$ denotes the number of combinations of $n$ distinct things taken $r$ at a time, then the domain of the function $g(x)={ }^{(16-x)} C_{(2 x-1)}$ is

The period of the function $f(x)=e^{\log (\sin x)}+(\tan x)^3-\operatorname{cosec}(3 x-5)$ is

If $f(x)$ is a real valued function defined by $f(x)=\frac{a x^{10}+b x^8+c x^6+d x^4+e x^2+12 x+15}{x}(x \neq 0)$ and $f(4)=-4$, then $f(-4)=$

If $f(x)$ and $g(x)$ are two real valued functions such that $f(x)=3 x-2$ and $g(x)=x^2+2$, then $[(g \circ f)+(f \circ g)](x)=$

Let $f: R \rightarrow R$ be a function defined by
$$ f(x)=\left\{\begin{array}{cc} x^2-4 x+3, & \text { if } x<2 \\ x-3, & \text { if } x \geq 2 \end{array}\right. $$
Then, the number of real numbers $x$ for which $f(x)=8$ is

The range of the real valued function $f(x)=\frac{1}{x-|x|}$ is

If the function $f: R \rightarrow R$ is defined by
$$ f(x)= \begin{cases}2 x-3, & \text { if } x<-2 \\ x^2-1, & \text { if }-2 \leq x \leq 2 \\ 3 x+2, & \text { if } x>2\end{cases} $$
then $f$ is

If $\frac{6 x^4+13 x^3+2 x^2-x+3}{2 x^2+3 x-2}=f(x)+\frac{A}{a x-1}+\frac{B}{x+b}$, then $f(\mathrm{l})+a \cdot B+b \cdot A=$

The domain of the real valued function
\(f(x)=\frac{\sqrt{\log _{10}\left(\frac{x}{x-2}\right)}}{\sqrt{[x]^2-5[x]+6}} \text { is }\)
(Here, $[x]$ denotes the greatest integer function)

Which one of the following functions is a bijection?

The range of the function defined by

$$ f(x)=\left\{\begin{array}{lc} 2 x-3, & \text { if } x<-1 \\ 1-x^2, & \text { if }-1 \leq x \leq 1 \text { is } \\ 3 x^2+2, & \text { if } x>1 \end{array}\right. $$

If $\sinh x=-\frac{4}{3}$, then $\sinh 2 x+\cosh 2 x=$

The domain of the real valued function $f(x)=\frac{\sqrt{|x|-x}}{\sqrt{x-[x]}}$ is

If $f(x)=-|x|$, then $($ fofof $)(x)+($ fofof $)(-x)=$

If $t$ is a parameter, $A=(a \sec t, b \tan t)$, $B=(-a \tan t, b \sec t)$ and $O=(0,0)$, then the locus of the centroid of $\triangle O A B$ is

If $f:[2, \infty) \rightarrow R$ is defined by $f(x)=x^2-4 x+5$, then the range of $f$ is

The range of the function $f(x)=-\sqrt{-x^2-6 x-5}$ is

If $f: R \rightarrow R$ is defined by $f(x)=2 x+\sin x, x \in R$, then $f$ is

The domain of the function $f(x)=\sin ^{-1}\left(\log _2\left(\frac{x^2}{2}\right)\right)$ is

The domain of the real valued function $f(x)=\sqrt{\frac{2 x^2-7 x+5}{3 x^2-5 x-2}}$ is

The range of the real valued function $f(x)=|x-2|+|x-3|$ is

Assertion (A) $\operatorname{coth} x=\frac{1-k}{1+k}(0 < k < 2)$.
Reason (R) The graph of $y=\tanh x$ always lies between the lines $y=-1$ and $y=1$
The correct option among the following is

If $[x]$ denotes the greatest integer $\leq x$, then the range of the real valued function $f(x)=\frac{1}{\sqrt{x-[x]}}$ is

If $[x]$ represents the greatest integer function, then the set of all real values of $x$ for which $f(x)=\sqrt{\frac{[x]-x}{x-[x]}}$ is real is

If the minimum value of $\cos (\sinh (\log x)+\cosh (\log x))$ is $k$, then $\cosh (k+1)=$