List of top Mathematics Questions on Functions asked in AP EAPCET

For the real values of $x$, the set of values of $k$ for which the function \[ f(x)=\frac{x^2+x+1}{x^2+kx+1} \] takes all real values is

If \[ f(x)=|x-2|+|x+1|, \] then the minimum value of \(f(x)\) is:

The function \[ f(x)=\sin\left(\log\left(x+\sqrt{x^2+1}\right)\right) \] is

The domain of the real-valued function \[ f(x)=\cos^{-1}\left(\frac{2-x}{4}\right)+[\log(3-x)]^{-1} \] is:

The domain of the real valued function \( f(x)=\log_{x-1}(3x+1) \) is

If \( f:A\rightarrow B \), \( g:B\rightarrow C \) are two functions such that \( gof: A\rightarrow C \) is an onto function, then it is necessary that

Let $f$ be a function with domain $[0,7]$ and $g$ be a function defined by $g(x)=|2x+1|$. Then the domain of $(f\circ g)(x)$ is

A $\subseteq \mathbb{R}$ and $f:A \to \mathbb{R}$ is a function defined by $f(x)=\dfrac{x-1}{x+1}$. If the domain of the function $f(2x)$ is $B$, then $A \cap B =$

The domain of the function $f(x) = \sqrt{\log_{10} \left(\frac{5x - x^2}{4}\right)}$ is:

If $f : [1, \infty) \to [1, \infty)$ is defined by $f(x) = 2^{x(x-1)}$, then $f^{-1}(x) =$

Let \(f:\mathbb{R}\to \mathbb{R}\) be defined by \(f(x)=2x+3\). If \(\alpha,\beta\) are the roots of the equation \[ f(x^2)-2f\left(\frac{x}{2}\right)-1=0 \] then \(\alpha^2+\beta^2=\)

The range of the function \[ f(x)=\frac{x^2+x+1}{x^2-x+1} \] is

The domain of the real valued function \[ f(x)=\frac{\sqrt{\log_{0.5}(x-3)}}{\sqrt{x-1}} \] is

If a function \(f\) satisfies \(f(x+1)+f(x-1)=\sqrt{2}f(x)\), then \(f(x+2)+f(x-2)=\)

The domain of the real valued function \[ f(x)=\frac{\log_2(x+3)}{\sqrt{x^2+3x+2}} \] is

The domain of the real valued function \[ f(x)=\frac{\sqrt{2-x}+\sqrt{1+x}}{\sqrt{x+3}} \] is

Let \(f\) be a function defined by \[ f(xy)=\frac{f(x)}{y} \] for all positive real numbers \(x\) and \(y\). If \(f(30)=20\), then \(f(40)=\)

The range of the real valued function \(f(x)=\dfrac{x^2+x+1}{x}\) is

If a function \(f:\mathbb{R}-\{l\}\to \mathbb{R}-\{m\}\) defined by \[ f(x)=\frac{x+3}{x-2} \] is a bijection, then \(3l+2m=\)

Let \(f:\mathbb{R}-\left\{-\frac{1}{2}\right\}\to \mathbb{R}\) be defined by \[ f(x)=\frac{x-2}{2x+1} \] If \(\alpha,\beta\) satisfy the equation \[ f(f(x))=-x, \] then \[ 4(\alpha^2+\beta^2)= \]

If \[ f(x)=\log \left(\frac{2x^2-3}{x}+\sqrt{\frac{4x^4-11x^2+9}{|x|}}\right) \] then \(f(x)\) is

The set \[ \left\{x \in \mathbb{R} \,/\, \frac{\sqrt{|x|^2-2|x|-8}} {\log(2-x-x^2)} \text{ is a real number} \right\} \] is equal to:

The domain of the real valued function \[ f(x)=\sin\left(\log\left(\frac{\sqrt{4-x^2}}{1-x}\right)\right) \] is: