Which function is the inverse of f Superscript negative 1 Baseline (x) = negative one-fifth x minus four-fifths?

c on edge

f (x) = - 5x - 4

Step-by-step explanation:

We want to get the inverse of the following function:

f^-1 (x) = (-1/5) x - 4/5

To do that, we have to replace x with f (x) and f^-1 (x) with x, as follows:

x = (-1/5) f (x) - 4/5

And then solve for f (x), the inverse of f^-1 (x).

x + 4/5 = (-1/5) f (x)

f (x) = - 5x + (-5) 4/5

f (x) = - 5x - 4

To check our result we compute a pair (x, f (x))

x f (x)

1 - 5*1 - 4 = - 9

which has to be equivalent to (-9, 1) in the original function

x f^-1 (x)

-9 (-1/5) * (-9) - 4/5 = 1