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g(x)=2x+1, h(x)=5x^2+3x+7. Find f such that f(g(x))=h(x).
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I made up this exercise. If h(x) was 4x^2 4x 7, then i could easily find that f(x)=x^2 6.
But in this scenario, is it possible to find the function f when we were told that f(g(x)) = h(x)? Prove it's impossible if it's impossible, or show what f(x) would be and how you found it.
edit: extra question, if h(x) = 4x^2 4x 7, is f(x)=x^2 6 the only function that satisfies the composition equation? If so, can you prove it?
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