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

 
 Oct 9, 2019
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Let g(x) = ax + b. Then g(f(x)) would be a(2x-3) + b

a(2x-3) + b = 2ax -3a + b = 5-4x

The x coefficients must match up, and the constants must match up as well, so 

2ax = -4x

a = -2

We can then plug it into 2ax - 3a + b

-4x +6 + b = 5-4x

6 + b = 5

b = -1

so g(x) = -2x-1

x=4

g(x)= -2(4) - 1 = -8 - 1 = -9

 Oct 9, 2019

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