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

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

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