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For the functions f(x)=2x−2 and g(x)=6x2−3, find (g∘f)(x).

User AussieJoe
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Answer: To find (g∘f)(x), we need to first find the composite function g(f(x)):

g(f(x)) = g(2x - 2)

We can now substitute the expression for f(x) into g(x):

g(f(x)) = g(2x - 2) = 6(2x - 2)^2 - 3

Expanding the squared term, we get:

g(f(x)) = 6(4x^2 - 8x + 4) - 3

Simplifying and combining like terms, we get:

g(f(x)) = 24x^2 - 48x + 21

Therefore, (g∘f)(x) = 24x^2 - 48x + 21.

Explanation:

User Chris Hayden
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