Find g(x)?

Question

This function is given: f(g(x)) = 2e^{4x-x^2} dx and f(y) = e^y.

 

Now find g(x)?

Answer 1

f(g(x)) = 2e^{4x-x^2} = e^ln2e^{4x-x^2} = e^{ln2+4x-x^2}

 

Since the power is equal to y because of f(y) = e^y, y = g(x) = ln2 + 4x - x².