List of top Mathematics Questions on Functions asked in CBSE CLASS XII

Assertion (A): Let \( A = \{ x \in \mathbb{R} : -1 \leq x \leq 1 \} \). If \( f : A \to A \) be defined as \( f(x) = x^2 \), then \( f \) is not an onto function.
Reason (R): If \( y = -1 \in A \), then \( x = \pm \sqrt{-1} \notin A \).
Determine those values of $x$ for which $f(x) = \frac{2}{x} - 5$, $x \ne 0$ is increasing or decreasing.

Let A be the set of 30 students of class XII in a school. Let f : A -> N, N is a set of natural numbers such that function f(x) = Roll Number of student x.
Give reasons to support your answer to (i).

Find the domain of the function \( f(x) = \cos^{-1}(x^2 - 4) \).