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Find f(x) and g(x) such that h(x) = (f @ g)(x)

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2 Answers

Hi Keith,
 
We know h(x) = (6-8x)^2.
Also h(x) = (f@g)(x) and g(x)=6-8x.
 
So for the composite function f@g(x), we can replace g(x) by 6-8x,so we get
 
h(x)
= f(6-8x) = (6-8x)^2.  ---(1)
 
since the question wants you to find f(x), we can simply replace 6-8x by x.
 
so from (1), we get
f(x) = x^2
 
 
Hi Keith;
g(x)=(6-8x)
f(x)=?
(f@g)x=h(x)=(6-8x)(6-8x)=(6-8x)2
f(x)=(6-8x)