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(a) if g(x) = 3x + 1 and h(x) = 9x2 + 6x + 7, find a function f such that f ∘ g = h. (think about what operations you would have to perform on the formula for g to end up with the formula for h.)

Answer :

Let's say that f(x) = ax^2 + bx + c

if f(g(x)) = 9x^2 + 6x + 7:
a(3x + 1)^2 + b(3x + 1) + c = 9x^2 + 6x + 7
9ax^2 + 6ax + a + 3bx + b + c = 9x^2 + 6x + 7
Comparing the two equations, we can see that a = 1, b = 0 and c = 6, therefor f(x) = x^2 + 6

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