Comment
Share
Q)

# If $f : R \to R$ be given by $f(x) = (3-x^3)^{\frac{1}{3}}$, then evaluate $f o f(x)$

$(A)\; x^{\frac{1}{3}}$
$(B)\; x^3$
$(C)\; x$
$(D)\; (3-x^3)$

• Given two functions $f : A \to B$ and $g: B \to C,$ then composition of $f$ and $g, gof : A \to C$ by $gof(x) = g(f(x))$ for all $x \in A$. Therefore it follows that $fof = f(f(x)).$
Given a function $f : R \to R$ be given by $f(x) = (3-x^3)^{\frac{1}{3}}$
we know that $(fof)(x) = f(f(x))$
$\implies fof = f((3 - x^3)^{1/3}) = [3 - ((3-x^3)^{1/3})^3]^{1/3}$
$\implies fof = [3 - (3-x^3)]^{1/3} = (x^3)^{1/3} = x$
$\therefore (fof)(x) = (C)x$ is the correct answer.