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Provide solution for RD Sharma Maths Class 12 Chapter Functions Exercise 2.2 Question 5.

Answers (1)

Answer : $f\; o\; g (2)=633$

$g\; o\; f (1)=2188$

Hint : $g\; o\; f$ means $f(x)$ function is in $g(x)$ function

$f\; o\; g$ means $g(x)$ function is in $f(x)$ function

Given : $f:R\rightarrow R ; f(x)=x^{2}+8$

$g:R\rightarrow R ; g(x)=3x^{3}+1$

Solution :

First, we find $f\; o\; g$

$f\; o\; g(x)=f(g(x))=f(3x^{3}+1)$

$f\; o\; g(x)=(3x^{3}+1)^{2}+8$ $\because [(a+b)^{2}=a^{2}+b^{2}+2ab]$

$f\; o\; g(2)=(3\times(2)^{3}+1)^{2}+8$

$=\left ( 3 \times 8+1 \right )^{2}+8$

$=(25)^{2}+8$

$=625+8$

$f\; o\; g(2)=633$

Similarly,

$g\; o\; f(x)=g(f(x))=g(x^{2}+8)=3(x^{2}+8)^{3}+1$

$g\; o\; f(1)=3(1+8)^{3}+1\Rightarrow 3(9)^{3}+1$

$=3\times 729+1$

$=2188$

Hence, $f\; o\; g(2)=633 \; \text {and} \; g\; o\; f(1)=2188$

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