The function h ( x ) = ( x + 7 ) 4 can be expressed in the form f ( g ( x ) ) where f ( x ) = x 4 , and g ( x ) is defined below:

Question

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Answer 1

maybe skip the beginning & middle and go to the very end for the answer, but for what it's worth are some further perhaps unnecessary details

h(x) = f(g(x)) = (x+7)^4 = (x+7)^2(x+7)^2= (x^4+14x + 49)(x^4+14x +49)

= x^8 + 28x^3 + 196x^2 + 1372x + 2401

f(x)= x^4

g(x) =a value let's call z such that f(z) = z^4 = h(x)

z=(x+7)

f(g(x) =f(z) = f(x+7) = (x+7)^4 = h(x)

g(x) = x+7