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Composite Function

f:R→ R define...

Question

$f : R \to R$ defined as under: $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} x - 4, & x < - 9 x^{2} - 1, & x ϵ [- 9, 9] 2 x + 5 & x > 9 \end{matrix}$ Evaluate $(f o f) 5$

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Solution

Using given definition of $f (x)$
$(f o f) 5 = f [f (5)] = f [25 - 1]$
$= f (24) = 2 (24) + 5 = 53$

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