Question

What is the inverse of f(x)=5/x+2−4?

Answer 1

I will assume you meant:
f(x)=5/(x+2)−4 or y = 5/(x+2)−4

inverse:
x = 5/(y+2) - 4
x + 4 = 5/(y+2)
xy + 2x + 4y + 8 = 5
xy + 4y = -2x - 3
y = (-2x - 3)/(x + 4) or f^-1 (x) = (-2x - 3)/(x + 4)

check: let x = 3, f(x) = 5/5 - 4 = -3
f^-1 (-3) = (-2(-3) - 3)/(-3 + 4) = 3/1 = 3 , looks good

Answer 2

The inverse of f(x)=5/x+2−4 is f^-1(x)=5/(x+4)-2.