Question: Suppose that g ( x ) = 2 x + 1 h ( x ) = 4 x 2 + 4 x + 5. Find

Suppose that

g(x) = 2x + 1
h(x) = 4x2 + 4x + 5.

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.)

f(x) =

Now suppose that

f(x) = 4x + 5
h(x) = 4x2 + 4x + 1.

Use the same sort of reasoning to find a function g such that

f g = h.

g(x) =

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