GATE Civil Engineering (CE) 2020 Shift 2 Solved Paper

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Question : 5 of 65

Marks: +1, -0

If

f(x)=x^{2}

for each

x ∈(-∞, ∞)

, then

\;{f(f(f(x)))}/{f(x)}

is equal to

$(f(x))^{4}$
$(f(x))^{2}$
$(f(x))^{3}$
$f(x)$

Solution:

F(x)=x^{2}

f(f(x))=fofo(x)=(x^{2})^{2}=x^{4}

f(f(f(x))))=

fofofo

(x)=(x^{4})^{2}=x^{8}

\;{f(f(f(x)))}/{f(x)}=\;{\;\text " fofofo "\;(x)}/{f(x)}=\;{x^{8}}/{x^{2}}

=x^{6}=(f(x))^{3}

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