JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

Let

R

be the set of real numbers and the functions

f: R \rightarrow R

and

g: R \rightarrow R

be defined by

f(x)=x^2+2 x-3

and

g(x)=x+1

. Then, the value of

x

for which

g(f(x))=f(g(x))

View answer and explanation

Correct option: A

-1

Option A (-1) is correct because substituting x = -1 into the equation g(f(x)) = f(g(x)) satisfies the equality.

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f:(-\infty, 2] \longrightarrow(-\infty, 4]

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f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

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

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

f: R \rightarrow R

f(x)=x^4

f(x)=(x+1)^2-1(x \geq-1)

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