JEE MATHEMATICS MCQ: FUNCTIONS

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Analyzing +4 | -1

Let

A=[-1,1], B=[-1,1], C=[0, \infty)

. If

R_1=\left\{(x, y) \in A \times B: x^2+y^2=1\right\}

and

R_2=\left\{(x, y) \in A \times C: x^2+y^2=1\right\}

, then

View answer and explanation

Correct option: D

R_2

defines a function from

A

onto

C

Option C (

f(x)=x^m, g(x)=x^n, m \neq n, m, n \in I

) is correct because the composition of these functions is commutative, i.e.,

(f \circ g)(x) = (g \circ f)(x)

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f\left( x \right) = x - \left[ x \right]

{f^{ - 1}}\left( x \right)

f: R \rightarrow R

f(x)=x^4

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S=\left\{x: f(x)=f^{-1}(x)\right\}