Question

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

Answer 1

-5/(x+4) is the inverse of the f(x)

Answer 2

Answer:

Therefore the function which is the inverse of $f^{-1}(x) = -(\frac{x + 4}{5})$ is, let us say, g(x) = -5x - 4

Step-by-step explanation:

The given function is $f^{-1}(x) = \frac{-1}{5}x - \frac{4}{5} = \frac{-x - 4}{5}$

$Let \hspace{0.1cm} y = f^{-1} (x) = (\frac{-x-4}{5} ) = - (\frac{x+4}{5} )$

To find the inverse of the above function we first substitute y with x and x with y.

This gives us $x = -(\frac{y+ 4}{5} )$

Now the next step is to simplify the above expression and get the value of y in terms of x.

Thus we get    -5x = y + 4    ⇒   y = -5x - 4.

Therefore the function which is the inverse of $f^{-1}(x) = -(\frac{x + 4}{5})$ is, let us say, g(x) = -5x - 4