What is the inverse of the following function?

f(x)=1x−5+2

Fist we are gonna simplify the function

f(x) = 1x - 5 + 2

Simplify 1 • x - 5 + 2

Multiply 1 • x
= x

= x - 5 + 2

Add the constants - 5 + 2
= -3

= x - 3

Inverse of function y = f(x) and x = g(y)

f(x) = x - 3

Or

y = x - 3

Replace x with y

x = y - 3

Solve for y, x = y - 3

x + 3

Therefore the inverse of f(x) = 1x - 5 + 2
Is g(y) = x + 3