Question

What is the inverse function of `f(x) =1/x`?

Answer 1

`f^-1 = 1/x`

Explanation:

Given: `f(x) = 1/x`

To find the inverse function, first let `f(x) = y: " "y = 1/x`

Switch `x " and " y: " "x = 1/y`

Solve for `y`, by multiplying both sides by `y`:

`x * y = 1/cancel(y) *cancel(y)/1`

`xy = 1`

Divide both sides by `x: " "(cancel(x)y)/cancel(x) = 1/x`

`f^-1 = 1/x`