Question

Use the functions f(x)=x+4 and g(x)=2x-5 to find the specified functions.

(g x f)^-1

Answer 1

Please state in words your notation

(g x f)^-1 I assume you do not mean the reciprocal of g times f.

Answer 2

let y = g x f
= (x+4)(2x-5)

y = 2x^2 + 3x - 20

so the inverse of that is
x = 2y^2 + 3y - 20
2y^2 + 3y - 20 - x = 0

which by the way is not a function

to solve for y you will have to use the quadratic formula and

y = (-3 ± √(9-8(-20-x))/4
etc.