List of top Mathematics Questions on Functions asked in AP EAPCET

If $ 0 \le x \le 3,\ 0 \le y \le 3 $, then the number of solutions $(x, y)$ for the equation: $$ \left( \sqrt{\sin^2 x - \sin x + \frac{1}{2}} \right)^{\sec^2 y} = 1 $$
The domain of the real valued function $ f(x) = \frac{3}{4 - x^2} + \log_{10}(x^3 - x) $ is
A real valued function $ f: A \to B $ defined by $ f(x) = \frac{4 - x^2}{4 + x^2} \ \forall x \in A $ is a bijection. If $ -4 \in A $, then $ A \cap B = $
Let \( f(x) = 2x^3 - 3x \neq 4 \). Then the inverse function \( f^{-1}(x) \) is:
Let \( f(x) = 3 + 2x \) and \( g_n(x) = (f \circ f \circ \dots \text{n times}) (x) \). If for all \( n \in \mathbb{N} \), the lines \( y = g_n(x) \) pass through a fixed point \( (a, \beta) \), then \( \alpha + \beta = ? \)

Let \( a>1 \) and \( 0<b<1 \). -∞\( f : \mathbb{R} \to [0, 1] \) is defined by \( f(x) = \begin{cases} a^x & \text{if } x<0 b^x & \text{if } 0 \leq x \leq 1 \end{cases} \), then \( f(x) \) is:

For \( x \in \mathbb{R} \), if \( f(x) = \sqrt{\log_{10} \left( \frac{3-x}{x} \right)} \), then the domain of \( f \) is:
If \( f(x) = x^3 - x \) and \( g(x) = \sin(2x) \), then \( f(g\left(\frac{\pi}{12}\right)) \) is:
$f\left(x\right) = \frac{x}{e^{x}-1} + \frac{x}{2} + 2 \cos^{3} \frac{x}{2} $ on $R-\left\{0\right\} $ is
$D = \left\{x\in\mathbb{R}: f\left(x\right) =\sqrt{\frac{x - \left|x\right|}{x - \left[x\right]}} \text{is defined} \right\}$ and $C$ be the range of the real function $g(x) = \frac{2x}{4 + x^{2}}$. Then $D \cap C$