If is the inverse of a function

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

Problem

If gg is the inverse of a function ff, which one of the following statements is always true for all admissible xx? (a) f(g(x))=g(f(x))f\bigl(g(x)\bigr)=g\bigl(f(x)\bigr) (b) f(g(x))=x and g(f(x))=xf\bigl(g(x)\bigr)=x \text{ and } g\bigl(f(x)\bigr)=x (c) f(g(x))=x onlyf\bigl(g(x)\bigr)=x \text{ only} (d) g(f(x))=x onlyg\bigl(f(x)\bigr)=x \text{ only}

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