Question

find the inverse of the function f(x) = x^2 + 7x

Answer 1

This is NOT a one-to-one function and so the inverse does not exist.
This is a quadratic function which when you plot it will be a vertical parabola.
If you draw a horizontal line sometimes the line will cut the parabola at two different points. Therefore, the function fails the horizontal line test for one-to-one function.