Question

Find fog and gof when f(x) = 2x +1 and g(x) = x

2

-2.​

Answer 1

$\displaystyle \sf{fog(x) = {2x}^{2} - 3 \: \: \: and \: \: gof(x) = {4x}^{2} + 4x - 1 }$

Correct question : Find fog and gof when f(x) = 2x +1 and g(x) = x² - 2

Given :

f(x) = 2x + 1 and g(x) = x² - 2

To find :

$\displaystyle \sf{fog(x) \: and \: gof(x) }$

Solution :

Step 1 of 2 :

Write down the given functions

Here it is given that ,

f(x) = 2x + 1 and g(x) = x² - 2

Step 2 of 2 :

$\displaystyle \sf{Find\:\:\: fog(x) \: and \: gof(x) }$

${\sf fog(x)}$

$\sf \: = \:f\bigg(g(x)\bigg)$

$\sf = f( {x}^{2} - 2)$

$\sf = 2( {x}^{2} - 2) + 1$

$\sf =2{x}^{2} -4 + 1$

$\sf =2{x}^{2} -3$

$\sf{ \therefore\:\: fog(x) = {2x}^{2} - 3 \: \: }$

Now we have

$\sf gof(x) \:$

$\sf = \:g\bigg(f(x)\bigg)$

$\sf = \:g(2x + 1)$

$\sf = {(2x + 1)}^{2} - 2$

$\sf = {4x}^{2} + 4x + 1 - 2$

$\sf = \: {4x}^{2} + 4x - 1$

$\sf{ \therefore\:\: gof(x) = {4x}^{2} + 4x - 1 \: \:}$

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Answer 2

Step-by-step explanation:

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