List of top Mathematics Questions on Functions asked in AP EAPCET

If \( f(x) = \sqrt{x} + \sin x \), then all the points of the set \( \left( x, f(x) \right)/f'(x) = 0 \) lie on:
A function \( f(x) \) is defined as: \[ f(x) = \begin{cases} ax^2 + bx + c, & x \leq -1
2x^2 + 4x + 1, & -1<x<1
cx^2 + bx + a, & x \geq 1 \end{cases} \] If \( f(x) \) is continuous on \( \mathbb{R} \) and \( \lim_{x \to -\frac{3}{2}} f(x) = 14 \), then \( \lim_{x \to 2} f(x) = \):
\(f(x)\) is a continuous function on \(\mathbb{R}\) and \(y = f(x)\) is a curve. If \((\alpha, \beta)\) is a point such that \(\beta = f(\alpha)\) and \(p\alpha + m\beta + n = 0\ (p \ne 0, m \ne 0)\), then which one of the following is True?
If a real valued function \( f \) is defined by \( f(x) = \frac{ax + \sqrt{a^2 - x^2}}{bx} \), then \( f \) is:
Let \([t]\) represent the greatest integer not exceeding \( t \) and \( C = 1 - 2e^2 \).
If the function \[ f(x) = \begin{cases} [e^x], & x < 0 \\ ae^x + [x - 2], & 0 \leq x < 2 \\ [e^x] - C, & x \geq 2 \end{cases} \] is continuous at \(x = 2\), then \(f(x)\) is discontinuous at:
Let \( A \subseteq \mathbb{R}, B \subseteq \mathbb{R} \) and \( f : A \to B \) be defined by \( f(x) = x^2 - 3x + 2 \). If \( f \) is a bijection, then
If \( f(a) = \log \left| \frac{1 - a}{1 + a} \right| \) for \( a \neq \{-1, 1\} \), then the set of values of all \( a \), for which \( f\left( \frac{2a}{1 + a^2} \right)>0 \) is:
If $f(g(x+y)) = f(g(x)) + f(g(y))$, $g(1)=2$, $f(2)=1$, then $g(f(x))$ is discontinuous on:
If \( f(x) \) is the signum function, then in terms of \( f(x) \), the constant function \( g(x)=1, \ \forall x \in \mathbb{R} \) is:
Match the ranges of the functions given in List - A with those of the items given in List - B.
Match the ranges of the functions given
Assertion (A): Every rational function is continuous at every real number \(x\) at which it is defined.
Reason (R): Every rational function is a quotient of two polynomials.
If \( f:\mathbb{R} \to \mathbb{R} \) is defined by \( f(x+y) = f(x) + f(y) \ \forall x, y \in \mathbb{R} \) and \( f(1) = 7 \), then \(\sum\limits_{r=1}^n f(r) =\)
Let \( x \) be a real number and \( -2<x<2 \). When \( \frac{x+1}{(x+3)(x-2)} \) is expanded in powers of \( x \), then the coefficient of \( x^3 \) is:
If \( f : \mathbb{R} \setminus \{0\} \to \mathbb{R} \) is defined by \( f(x) = x + \frac{1}{x} \), then the value of \( \left(f(x)\right)^2 \) is:
For \( x \in \mathbb{R} \), the minimum value of \( \frac{x^2 + 2x + 5}{x^2 + 4x + 10} \) is:
If \( f(0) = 0, f(1) = 1, f(2) = 2 \) and \( f(x) = f(x-2) + f(x-3) \) for \( x = 3, 4, 5, \dots \), then find \( f(10) \).
Let \( f: \mathbb{R} \rightarrow \mathbb{R} \) be a function defined by \( f(x) = \frac{2x+1}{3} \). If \( \alpha \) is an element in the domain of \( f \) whose image is \( \frac{1}{\alpha} \), then the sum of all possible values of such \( \alpha \) is
The domain of the function $ y = f(x) $, where $ x $ and $ y $ are related by $ 2^x + 2^y = 2 $, is:
The range of the function $ f(x) = \begin{cases} 4x - 1, & x>3 \\ x^2 - 2, & -2 \leq x \leq 3 \\ 3x + 4, & x<-2 \end{cases} $ is:
If $ \sin x \cosh y = \cos \theta $ and $ \cos x \sinh y = \sin \theta $, then find $ \sin^2 x + \cosh^2 y $.
Let \(f(x)=\sqrt{\frac{x+1}{x+3}}\) and \(g(x)=\sqrt{\frac{2-x}{x+3}}\) be two real valued functions. Then the domain of \(\frac{f}{g}\) is:
If the function \(f:\mathbb{R}\to\mathbb{R}\) is defined as \(f(x)=x^2-2x-3\), then \(f\) is:
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