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RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS1 Mark
Question
State True or False for the statements.
The composition of functions is commutative.
✓

Answer

False.
Solution:
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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