Question

I have no idea how to do this question:

Write two functions f(x) and g(x) for which (f*g)(x)= 2x²+11x-6. Tell how you determined f(x) and g(x).

Can you answer this?

Answer 1

You can take for g(x) an arbitrary function with an inverse g_inv(x). Then you take f(x) to be

f(x) = 2 (g_inv(x))^2 + 11 g_inv(x) - 6

f(g(x)) = 2 (g_inv(g(x)))^2 +
11 g_inv(g(x)) - 6 =

2x^2+11x-6

E.g. If you take g(x) = Log(x), then g_inv(x) = Exp(x) and

f(x) = 2 Exp(2x) + 11 Exp(x) - 6

Answer 2

Is there any simpler way to solve this problem?

Answer 3

I recommend that you study this general solution as long as it takes for you to understand it.

Students are given problems in order to master maths. Trying to find a solution to a problem without understanding the issues involved is pointless.