First slide

Functions (XII)

Question

$If f : R \to R, f (f (x)) = (f (x))^{2}, then f f f (x) is not equal to$

Moderate

A

${(f (x^{4}))}^{2}$
B

$(f (x))^{4}$
C

${(f (x^{2}))}^{2}$
D

$f (x^{4})$

Solution

$Replacing f (x) by x, we have f (x) = x^{2}$
$Now f (f (x)) = f (x^{2}) = {(x^{2})}^{2} = x^{4} \Rightarrow f (f (f (x))) = f (x^{4}) = {(x^{4})}^{2} = x^{8} = (f (x))^{4}$
$n o w {(f (x^{2}))}^{2} = x^{8^{}}$ $a n d f (x^{4}) = x^{8}$

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