Functions - Calculus - Mathematics Previous Year Questions

If \(f:R \to R\) is defined by \(f(x) = |x|\), then

If \(f(x)\) satisfies the relation \(2f(x) + f(1 - x) = {x^2}\) for all real x, then \(f(x)\) is

The approximate value of \((0.007)^{1/3}\) is

If \(f(x)+2f(1-x)=x^2+5,\forall\) real values of \(x\), then \(f(x)\) is given by

The range of \(x\) which satisfy the inequation : \(-5 \leq \frac{2-3 x}{4} \leq 9\) is

$$\text { Which of the following function is injective? }$$

The domain of the function \(y=\frac{1}{\log _{10}(3-x)}+\sqrt{x+7}\) is

Which of the following is not a homogenous function of \(x\) and \(y\)

Let \(f: R \rightarrow R\) be a function defined by \(f=\frac{e^{|x|}-e^{-x}}{e^x+e^{-x}}\) then

A function $f$ from the set of natural numbers to integers defined by

$$f(n)=\left\{\begin{array}{l} \[\frac{n-1}{2}, \quad \text { when } n \text { is odd } \\\] \[-\frac{n}{2}, \quad \text { when } n \text { is even }\] \end{array} \quad\right. \text { is }$$

If \(2 f\left(x^2\right)+3 f\left(\frac{1}{x^2}\right)=x^2-1, \forall x \in R-\{0\}\), then \(f\left(x^8\right)\) is equal to

The function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x)=\frac{x}{x^2+1} \quad \forall x \in \mathbb{R}$ is