List of top Mathematics Questions on Functions asked in MET

Let \( f(x) = \sqrt{1 + x^2} \), then

If \(n \in \mathbb{N}\), then \(|\sin nx|\)

If \(f(x) = \cos[\pi^2]x + \cos[-\pi^2]x\), then

The range of \(f(x) = \sec\left(\frac{\pi}{4}\cos^2 x\right)\), \(-\infty<x<\infty\) is

The domain of the function \(f(x) = \frac{\sin^{-1}(3 - x)}{\log(|x| - 2)}\) is

If \(f(x) = (a - x^n)^{1/n}\), where \(a>0\) and \(n\) is a positive integer, then \(f[f(x)]\) is equal to

A function \(f(x) = \frac{x^2 - 3x + 2}{x^2 + 2x - 3}\) is

Let \(h(x) = \min(x, x^2)\), for every real number \(x\). Then,

If \[ f(x) = \frac{e^{1/x} - 1}{e^{1/x} + 1}, \quad x \neq 0 \quad \text{and} \quad f(0) = 0, \] then \(f(x)\) is:

The domain of definition of the function \[ f(x) = \frac{1}{| |x| - 1 | - 5} \] is:

The domain of the function \( f(x) = \frac{\sqrt{9 - x^2}}{\sin^{-1}(3 - x)} \) is ________.

The range of the function $f(x)=\logₑ(3x²-4x+5)$ is ________.