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

Question

shtirl

3 months ago

10

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

egative 1 Baseline (x) = negative one-fifth x + four-fifths

Mathematics

2 answers:

Zina [12.3K] · Answer 1 · 2026-02-17T12:51:47+03:00

Zina [12.3K]3 months ago

7 0

Answer:

The solution is "-5x-4"

Step-by-step explanation:

Given:

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

resolve the provided equation:

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

Let

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

find the inverse of the function above:

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

lawyer [12.5K] · Answer 2 · 2026-02-17T12:54:18+03:00

The inverse of the function is $g (x)=-5x-4$ . To find this, we start with the given function: $f^{-1}(x)=-\frac{1}{5}\ x-\frac{4}{5}$ . Let us denote $y=f^{-1}(x)$ for further calculations. Substituting will yield the equation: $y=\frac{-x-4}{5}$ . To proceed with determining the inverse, exchange x and y in the equation. The result of this substitution leads to: $x=\frac{-y-4}{5}$ , then continues until we derive the value for y as: $g (x)=-5x-4$ . This gives us the inverse function as $g (x)=-5x-4$ .