Question:
If $f: R \rightarrow R$ be defined by $f(x)=\left(3-x^{3}\right) 1 / 3$, then find $f \circ f(x)$.
Solution:
$(f o f)(x)=f(f(x))$
$=f\left(\left(3-x^{3}\right)^{\frac{1}{3}}\right)$
$=\left[3-\left(\left(3-x^{3}\right)^{\frac{1}{3}}\right)^{3}\right]^{\frac{1}{3}}$
$=\left[3-\left(3-x^{3}\right)\right]^{\frac{1}{3}}$
$=\left(x^{3}\right)^{\frac{1}{3}}$
$=x$
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