KARNATAKA-2nd-PUC-2023-Mathematics-Sample-Paper
KARNATAKA 2nd PUC 2023 Mathematics Sample Paper
Question 21
Find $gof$ and $fog$, if $f: R \to R$ and $g: R \to R$ are given by $g(x) = x^{\dfrac{1}{3}}$ and $f(x) = 8x^3$
Solution
The correct answer is $gof(x) = 2x$ and $fog(x) = 2x$
Explanation
Given $g(x) = x^{\dfrac{1}{3}}$ and $f(x) = 8x^3$
$gof(x)=g(f(x))$ = $(8x^3)^\dfrac{1}{3}$ = $2x$
$fog(x)=f(g(x))$ = $8(x^\frac{1}{3})^3$ = $8x$
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