For and , which of the following statements is…

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

For

f(x)=\dfrac{3x-4}{5}

and

g(x)=\dfrac{5x+4}{3}

, which of the following statements is correct? (a)

f\bigl(g(x)\bigr)=x

for all

x

, but

g\bigl(f(x)\bigr)\neq x

for some

x

(b) Neither

f\bigl(g(x)\bigr)

nor

g\bigl(f(x)\bigr)

equals

x

for every

x

(c) Both

f\bigl(g(x)\bigr)=x

and

g\bigl(f(x)\bigr)=x

for all

x

in their domains (d)

g\bigl(f(x)\bigr)=x

for all

x

, but

f\bigl(g(x)\bigr)\neq x

for some

x

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