List of top Mathematics Questions on Relations and functions asked in TS EAMCET

The sum of all the integers in the domain of the real valued function \[ f(x)=\sqrt{\log_{\frac13}\left(\frac{9x-30}{x-26}\right)} \]

If $f(x)$ is a linear polynomial such that \[ f(ax+by)=af(x)+bf(y) \] for all $x,y\in\mathbb{R}$. If $f(0)=7$ and $f'(0)=5$, then \[ \frac{f(1)+f(-1)}{a+b}= \]

The domain of the real valued function \[ f(x)=\cos^{-1}\!\left(\log_{5}\frac{x}{5}\right)+\log_{5}\!\left(\cos^{-1}\frac{x}{5}\right) \] is:

If $f:\mathbb R\to\mathbb R$ is defined by \[ f(x)=|x| \] and $A=(0,1)$, then $f^{-1}(A)$ is:

If $f:\mathbb{R}-\left\{\frac{2a}{3}\right\}\rightarrow \mathbb{R}$ is a function defined by \[ f(x)=\frac{2x+a}{3x-2a} \] and $(f\circ f)(x)=x$ for all $x\in \mathbb{R}-\left\{\frac{2a}{3}\right\}$, then $f(3)=$}

If $f:\mathbb{R}\rightarrow\mathbb{R}$ and $g:\mathbb{R}\rightarrow\mathbb{R}$ are defined by \[ f(x)=|x+1| \] and \[ g(x)= \begin{cases} e^{-x}, & x\le 0\\ x-1, & x>0 \end{cases} \] then $(f\circ g)(-2)+(g\circ f)(2)=$}

If the domain and the range of the real-valued function \[ f(x)=\frac{1}{\sqrt{|x|-[x]}} \] are $A$ and $B$, respectively, then \[ A\cap B = \ ? \] (Here, $R^{+}$ denotes the set of positive real numbers and $Z^{+}$ denotes the set of positive integers.)

A real valued function $f$ defined by \[ f(x)=|x|-x \] is

A function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = \begin{cases} 2x+3, & x \le 4/3 \\ -3x^2+8x, & x>4/3 \end{cases}$ 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 $2b =$

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

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

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

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

The domain of the real valued function: \[ f(x) \;=\; \sqrt[3]{\frac{x \,-\, 2}{2x^2 \,-\, 7x \,+\,5}} \;+\; \log\bigl(x^2 \,-\, x \,-\, 2\bigr). \]

Define $ f: \mathbb{R} \to \mathbb{R} $ by \[ f(x) = \begin{cases} \frac{1 - \cos 4x}{x^2}, & x < 0 \\ a, & x = 0 \\ \frac{\sqrt{x}}{\sqrt{16 + \sqrt{x}} - 4}, & x > 0 \end{cases} \] Find the value of $ a $ such that $ f $ is continuous at $ x = 0 $.

f is a real valued function satisfying the relation $f\bigl(3x + \tfrac{1}{2x}\bigr) \;=\; 9x^2 + \tfrac{1}{4x^2}$. If $f\bigl(x + \tfrac{1}{x}\bigr) = 1$ then $x =$ ?