Question

Find inverse f(x)=2/-2x-5

Answer 1

start with y = 2/(-2x-5)
and switch variables, then solve for y again.
x = 2/(-2y-5)
2y+5 = -2/x
2y = -2/x - 5
y = -1/x - 5/2 = -(5x+2)/(2x)
so that means that
f^{^-1}(x) = -(5x+2)/(2x)

you should always check your results, to make sure that
f^{^-1}(f(x)) = f(f^{^-1}(x)) = x

Answer 2

I will assume you meant:
f(x)=2/(-2x-5)

let y = 2/(-2x-5)

step1: interchange the x and y variables
---> x = 2/(-2y-5)

step2: solve this new equation for y
2 = - 2xy - 5x
2xy = -2 - 5x
y = (-2 - 5x)/(2x)

f ^-1 (x) = (-2 - 5x)/(2x)