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How do I find (fog)(x) with the given equations f(x)=8x+2 and g(x)=x^2-8 ?

normally I would know hoe to solve this is a number was in the place of the x but since the x is there, I'm stuck.
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1 Answer

f(x) = 8x + 2
g(x) = x2 - 8
To take the composition of f and g (fog), replace the x in f(x) with g(x):
 
(fog)(x) = 8g(x) + 2                 [f(x) = 8x + 2]
 
(fog)(x) = 8(x2 - 8) + 2            [since g(x) = x2-8]
 
(fog)(x) = 8x2 - 64 + 2
 
(fog)(x) = 8x2 - 62
 
For a primer on composition of functions, check out the following: