Correct, so let's see what happens, if

function f multiplies the input by itself.

f(x) = x^2

f(g(x)) = (2x - 3)^2 = 4x^2 plus other stuff

So, multiplying by the input is not enough. The square of 2x is 4x^2, but we want 2x^2. What to do?

Answer: Take half the square.

1/2*(

2x)^2 = 2x^2

So, let's start with that (i.e., make f the function that outputs half of the input's square):

f(x) = 1/2*x^2

Now we have:

f(g(x)) = f(2x - 3) = 2x^2 - 6x + 9/2

Next step: what can be done about that -6x term, knowing that function f has 2x-3, to work with?

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