If f(x)=x+4 and h(x)=4x-1, find a function g such that g(f(x)) = h(x).
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beckden
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We get the above answer by noting that g(x) must be linear otherwise when applied to (x+4) we would not get another linear function.
So suppose g(x)=ax+b
g(f(x))=g(x+4)=a(x+4)+b=ax+4a+b
Now we are told that g(f(x))=4x-1
So
a=4 and 4a+b=-1
4(4)+b=-1
16+b=-1
b=-17
So our functiong g(x) must be
g(x) = 4x - 17
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Tushar Chandra
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It is given that f(x) = x + 4 and h(x) = 4x - 1. We have to find g(x) such that g(f(x)) = h(x)
g(x + 4) = 4x - 1
(4*(x + 4) - 17) = 4x + 16 - 17 = 4x - 1
The function g(x) = 4x - 17
One function g(x) that gives g(f(x)) = h(x) is g(x) = 4x - 17