Question

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

Answer 1

Answer:

The answer is "-5x-4"

Step-by-step explanation:

Given:

$\bold{f^{-1} (x)=(-\frac{1x}{5}-\frac{4}{5})}$

solve the above equation:

$\to f^{-1}(x)= \frac{-x-4}{5}\\\\\to f^{-1}(x)= -\frac{x+4}{5}$

Let

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

inverse the above function:

$\to x= -(\frac{y+4}{5})\\\\\to 5x= -(y+4)\\\\\to 5x= -y-4\\\\\to\boxed {y=-5x-4}$

Answer 2

Answer:

The inverse of the function is $g (x)=-5x-4$.

Step-by-step explanation:

The function provided is:

$f^{-1}(x)=-\frac{1}{5}\ x-\frac{4}{5}$

Let us assume that:

$y=f^{-1}(x)$

Then the equation will be:

$y=\frac{-x-4}{5}$

To compute the inverse of the function substitute x as y and y as x.

$x=\frac{-y-4}{5}$

Now solve for y as follows:

$x=\frac{-y-4}{5}$

$5x=-y-4$

$y=-5x-4$

Thus, the inverse of the function is $g (x)=-5x-4$.