If f : R → R be defined by

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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