List of top Mathematics Questions on Functions asked in AP EAPCET

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:
If a function \( f \) satisfies \( f(x+1) + f(x-1) = \sqrt{2}f(x) \), then \( f(x+2) + f(x-2) = \)
Given: $$ 3f(\cos x) + 2f(\sin x) = 5x $$ Find: $$ f'(\cos x) + f'(\sin x) $$
If a function \( f: \mathbb{R} - \{l\} \to \mathbb{R} - \{m\} \) defined by \( f(x) = \frac{x+3}{x-2} \) is a bijection, then \( 3l + 2m = \) ?
If $f(x) = ax^2 + bx + c$ for some $a, b, c \in \mathbb{R}$ with $a + b + c = 3$ and \[ f(x+y) = f(x) + f(y) + xy,\quad \forall x, y \in \mathbb{R} \] Then $\sum_{n=1}^{10} f(n) = $ ?
If $f(f(0)) = 0$, where $f(x) = x^2 + ax + b$, $b \neq 0$, then $a + b =$
If f is a relation from set of positive real numbers to the set of positive real numbers defined by \(f(x) = 3x^2-2\) then f is
If $f(x) = \sqrt{2 - x^2}$ and $g(x) = \log(1 - x)$ are two real-valued functions, then the domain of the function $(f+g)(x)$ is:
Let \(f: R \rightarrow R\) be defined by \(f(x) = 2x+3\). If \(\alpha, \beta\) are the roots of the equation \(f(x^2) - 2f(\frac{x}{2}) - 1 = 0\) then \(\alpha^2 + \beta^2 = \)
The range of the real valued function \( f(x) = \frac{x^2 + x + 1}{x} \) is
If $$ f(x) = \log\left(\left(\frac{2x^2 - 3}{x}\right) + \sqrt{\frac{4x^4 - 11x^2 + 9}{|x|}}\right) $$ then $ f(x) $ is:
Let $ f : \mathbb{R} - \left\{-\frac{1}{2}\right\} \rightarrow \mathbb{R} $ be defined by $$ f(x) = \frac{x - 2}{2x + 1} $$ If $ \alpha, \beta $ satisfy the equation $$ f(f(x)) = -x $$ then evaluate: $$ 4(\alpha^2 + \beta^2) $$
$\left\{ x \in \mathbb{R} \,\middle|\, \frac{\sqrt{|x^2 - 2|x| - 8}}{\log(2 - x - x^2)} \text{ is a real number} \right\} =$
The domain of the real valued function $f(x) = \sin\left(\log\left(\frac{\sqrt{4 - x^2}}{1 - x}\right)\right)$ is
Let \( f(x) = x^2 + \frac{1}{x^2} \) and \( g(x) = x - \frac{1}{x} \) for \( x \in \mathbb{R} \setminus \{-1, 0, 1\} \). Then, the local minimum of \( \frac{f(x)}{g(x)} \) is:
The domain of the real-valued function \(f(x) = \frac{\sqrt{\log_{0.5}(x-3)}}{\sqrt{x-1}}\) is: