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avatar+184 

Let $f(x) = 2x - 3$ and $g(f(x)) = 5-4x.$. Find $g(4)$.

 
 May 4, 2021
 #1
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We see $f(x)$ appears inside of $g(x)$, which is $g(f(x))$

 

Therefore we can conclude that

 

$g(2x-3)=5-4(2x-3)$

 

since we plug in the input of the $g(x)$ function

now we solve the $2x-3=4$, so we get $2x=7, x=7/2$ then we plug in 7/2 into the $5-4(2x-3)$ expression, 

 

 

this gives $5-4(7-3) = 5-4(4) = 4-16 = -12$
 

I get $\boxed{-12}$, however I suggest you check my work as I might have misunderstood, but this should give you an idea.

 
 May 4, 2021
 #2
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The answer was -9. 

 
 May 4, 2021

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