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Please solve rd Sharma class 12 chapter 2 exercise 2.3 question 1 maths textbook solution

Answers (1)

$f0g(x)=x and g0f(x) = x$ $f0g(x)=x and g0f(x) = x$

Hint : If $f:A\rightarrow B and g:B\rightarrow c$ two given functions then the composite of f and g denoted by g?f

$\therefore (gof):A\rightarrow C(gof)(x)=g{f(x)}x\epsilon A.$

and dom $(gof)=dom f$

Given: Here given that $f(x)=e^{x} and g(x)= \log_{e}e^{x}$ and

Here we have find out $f o g and g o f$

Solution:

Here first we will find out $f o g$

$f(x)=e^{x} and g(x)=\log_{e}X$

$\therefore f 0 g (x)=f{g{x}}$

$=f{loge^{x}}$

$=\log_{e}e^{x}$

Now, we find out g o f, we have,

Here we have,

$f(x)=e^{x}$ & $g(x)=loge^{x}$

$\therefore g o f(x) = g{f(x)}$

$=g{e^{x}}$

$=\log_{10}(e^{x})$

$=x$

$\therefore g o f = x$

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