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JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

if

f

and

g

are the function such that

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

for all

x

then

f

and

x

and

g

may be defined as

View answer and explanation

Correct option: D

\mathrm{f}(\mathrm{x})=x^m, g(x)=x^2+1

Option D is correct because the composition of functions

f(x) = x^m

and

g(x) = x^2 + 1

results in

(fg)(x) = (gf)(x)

for all x.

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