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RELATIONS AND FUNCTIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSRELATIONS AND FUNCTIONS1 Mark
Question
State True or False for the statements. The composition of functions is commutative.
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Answer

Let $f(x) = x^2$
and $g(x) = x + 1$
$fog(x) = f(g(x))$
$= f(x + 1)$
$= (x + 1)^2$
$= x^2 + 2x + 1$
$gof(x) $
$= g(f(x))$
$= g(x^2)$
$ = x^2 + 1$
Thus, $\text{fog}(\text{x})\neq\text{gof}(\text{x})$

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