If f(x)=3x-3 and g(x)= x^3 + 27, what is g(f(x))? a. 27x^3 b. 27x^3-81x^2+81x c. 9x^2-18x+36 d. 3x^3+78
f(x)=3x-3 and g(x)= x^3 + 27, g(f(x)) = g(3x-3) = (3x-3)^3 + 27 = 27(x-1)^3 + 27 = 27(x^3 - 3x^2 + 3x - 1) + 27 = 27(x^3 - 3x^2 + 3x - 1 + 1) = 27(x^3 - 3x^2 + 3x) = 27x^3 - 81x^2 + 81x
Question
Updated 6/22/2014 4:00:30 AM
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3
f(x)=3x-3 and g(x)= x^3 + 27,
g(f(x)) = g(3x-3) = (3x-3)^3 + 27
= 27(x-1)^3 + 27
= 27(x^3 - 3x^2 + 3x - 1) + 27
= 27(x^3 - 3x^2 + 3x - 1 + 1)
= 27(x^3 - 3x^2 + 3x)
= 27x^3 - 81x^2 + 81x
Confirmed by jeifunk [6/22/2014 4:03:27 AM]

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