d Problem: Functions f(x)=5^x-4 and g(x)=1+2x are given. Find (fog)(3). | Job Exam Rare Mathematics (JEMrare) - Solved MCQs
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Problem: Functions f(x)=5^x-4 and g(x)=1+2x are given. Find (fog)(3).

Problem: Functions\( f(x)=5^{x-4} \)     and ​\( g(x)=2x+1 \)​ are given. Find (fog)(3).

Solution:

 

It is a problem of composite functions !

Com-posit functions

We know that,

fog(x)=f(g(x))

So,

\[(fog)(x) =f(g(x))= 5^{(2x+1)-4}=5^{2x-3} \]

Now we have to find fog(3), so put x=3

we get

[\[(fog)(3) =f(g(3))= 5^{(2(3)+1)-4}=5^{2(3)-3}=5^3=125 \]

 

So, f0g(3)=125

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