If g(x) = 3x2 - 3 and g[f(x)] = 7x, then find f(x).

To find f(x), we first need to understand that g[f(x)] = 7x means that when we substitute f(x) into function g, we get 7x.

Given that g(x) = 3x^2 - 3, we can set this equal to 7x and solve for x:

3x^2 - 3 = 7x

Rearrange the equation to isolate terms involving x:

3x^2 - 7x - 3 = 0

This is a quadratic equation, but it doesn't have a simple solution for x.

However, we're looking for f(x), not x. We know that whatever f(x) is, when we substitute it into g(x), we get 7x. So, we can say that:

f(x) = sqrt[(7x + 3) / 3]

This is the function f(x) that, when substituted into g(x), gives 7x.