Relations and Functions

A function \(f: R^{+} \rightarrow R\) (where \(R^{+}\) is the set of all non-negative real numbers) defined by \(f(x)=4 x+3\) is :

Let the relation \(R\) on the set \(\text{M}=\left\{1,2,3,\ldots ,16\right\}\) be given by \(\text{R}=\left\{\left(x,y\right):4y=5x−3,x,y\in \text{M}\right\}\).

Then the minimum number of elements required to be added in \(R,\) in order to make the relation symmetric, is equal to

[JEE Main 2026, 22 Jan (Shift 1)]

A function \(\mathrm{f}:\mathrm{ℝ}\to \mathrm{ℝ}\) defined as \(\mathrm{f}(x)={x}^{2}-4x+5\) is :

The sum of absolute maximum and absolute minimum values of the function \(f(x)=\left|2 x^2+3 x-2\right|+\sin x \cos x\) in the interval \([0,1]\) is:

[JEE Main 2022, 24 Jun (Shift 1)]

Let \(f\text{ }:\text{ }{R}_{+}\text{ }\to \text{ }\left[5,\text{ }\infty \right)\) be defined as \(f\left(x\right)=9{x}^{2}+6x-5,\) where \({R}_{+}\) is the set of all non-negative real numbers. Then, \(f\) is

Let \(f: R^{+} \rightarrow[-5, \infty)\) be defined as \(f(x)=9 x^2+6 x-5\), where \(R^{+}\) is the set of all non-negative real numbers. Then, \(f\) is :

A function \(\mathrm{f}:\mathrm{ℝ}\to \mathrm{ℝ}\) defined as \(\mathrm{f}(x)={x}^{2}-4x+5\) is :

\(\begin{aligned}& A=\{1,2,3, \ldots, 10\}, \\& B=\left\{\frac{m}{n}, n>m, m, n \in A, \operatorname{gcd}(m \cdot n)=1\right\}\end{aligned}\)
Then no. of elements in \(\mathrm{B}=\) ? (22 Jan, Shift I, Memory Based)

A function \(f:{R}_{+}\to R\) where \({R}_{+}\) is the set of all non-negative real numbers) defined by \(f\left(x\right)=4x+3\) is:

If \(f:\mathrm{R}\to \mathrm{R}\), is given by \(f\left(x\right)={\left(3-{x}^{3}\right)}^{\frac{1}{3}}\), then \(f∘f\left(x\right)\) is equal to :

(i) If \(f:R\to R\) be defined as \(f(x)={x}^{2}\). then

Let R be the relation in the set N given by \(R={(a,b):a=b-2,b>6}\). Choose the correct answer from the following

[PYQ 2024, 2023, 2022]

If R be the relation in the set N given by \(R={(a,b):a=b-2,b>6}\), then

\(\text{ Let }A={a,b,c}\text{ and }R={(a,a),(a,b)(b,a)}\text{ then }R\text{ is }\)

In the function \(f:R\to R\), given by \(f(x)=5x\)

\(WhattypeofrelationisR={(a,b),(b,c),(b,a),(c,b)onthesetA={a,b,c}?\)

Let \([x]\) denote the greatest integer \(\leq x\), where \(x \in R\). If the domain of the real valued function \(f\left(x\right)=\sqrt{\frac{|[x]|-2}{|[x]|-3}}\) is \((-\infty, a) \cup[b, c) \cup[4, \infty), a

if \(\text{ }f:R\to R\) be such that \(\text{ }f(x)=5x+4\)then,\(\text{ }{f}^{-1}(x)=\)

If \(f:\mathrm{R}\to \mathrm{R},f(x)=\sin xandg:\mathrm{R}\to \mathrm{R},g(x)={x}^{2}\)

then \((f∘g)(x)\) is equal to: