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Need solution for RD Sharma Maths Class 12 Chapter Function Exercise 2.2 Question 6.

Answers (1)

Answer : $f\; o\; g=x \; \text {and}\; g\; o\; f=x$

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

$g(x)=\sqrt{x}$

Solution :

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

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

Similarly,

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

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

Thus

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

$x=x$

Hence proved functions are equal.

$f\; o\; g=x\; \text {and}\; g\; o\; f=x$

Posted by

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