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Need solution for RD Sharma Maths Class 12 Chapter Function Exercise 2.2 Question 7.

Answers (1)

Answer : $f\; o\; g \neq g\; o\; f$

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 : $f:R \rightarrow R$ defined by

$f(x)=x^{2}$

$g:R\rightarrow R$ defined by

$g(x)= x+1$

Solution :

$f\; o\; g(x)=f(g(x))=f(x+1)$

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

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

Similarly,

$g\; o\; f(x)=g(f(x))=g(x^{2})$

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

Now we have to make a comparison between eq. (i) and (ii)

$f\; o\; g(x) \neq g\; o\; f(x)$

$x^{2}+1+2x \neq x^{2}+1$

Hence proved $f\; o\; g \neq g\; o\; f$

Posted by

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