Question:
Let $f: R \rightarrow R: f(x)=\left(3-x^{3}\right)^{1 / 3}$. Find $f$ o $f$.
Solution:
To find: $f$ of
Formula used: (i) $f$ o $f=f(f(x))$
Given: (i) $f: R \rightarrow R: f(x)=\left(3-x^{3}\right)^{1 / 3}$
We have,
$f \circ f=f(f(x))=f\left(\left(3-x^{3}\right)^{1 / 3}\right)$
$f \circ f=\left[3-\left\{\left(3-x^{3}\right)^{1 / 3}\right\}^{3}\right]^{1 / 3}$
$=\left[3-\left(3-x^{3}\right)\right]^{1 / 3}$
$=\left[3-3+x^{3}\right]^{1 / 3}$
$=\left[x^{3}\right]^{1 / 3}$
$=x$
Ans) $f$ o $f(x)=x$
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