Answer:
[tex]f^{-1}(x)=-\frac{1}{5} x-\frac{4}{5}[/tex]
Step-by-step explanation:
It is called an inverse or reciprocal function of [tex]f[/tex] to another function [tex]f^{-1}[/tex] that fulfills that:
If [tex]f(a)=b[/tex], then [tex]f^{-1} (b)=a[/tex]
The inverse of [tex]f(x)=-5x-4[/tex] is:
We change the x for the y
[tex]x=-5y-4[/tex]
Now, let's clear y
[tex]y=\frac{x+4}{-5}[/tex]
Ordering
[tex]y = -\frac{1}{5} x-\frac{4}{5}[/tex]
So, the inverse of the function [tex]f(x)=-5x-4[/tex] is:
[tex]f^{-1}(x)=-\frac{1}{5} x-\frac{4}{5}[/tex]
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