Respuesta :
Answer:
The inverse of the function is [tex]g (x)=-5x-4[/tex].
Step-by-step explanation:
The function provided is:
[tex]f^{-1}(x)=-\frac{1}{5}\ x-\frac{4}{5}[/tex]
Let us assume that:
[tex]y=f^{-1}(x)[/tex]
Then the equation will be:
[tex]y=\frac{-x-4}{5}[/tex]
To compute the inverse of the function substitute x as y and y as x.
[tex]x=\frac{-y-4}{5}[/tex]
Now solve for y as follows:
[tex]x=\frac{-y-4}{5}[/tex]
[tex]5x=-y-4[/tex]
[tex]y=-5x-4[/tex]
Thus, the inverse of the function is [tex]g (x)=-5x-4[/tex].
Answer:
The answer is "-5x-4"
Step-by-step explanation:
Given:
[tex]\bold{f^{-1} (x)=(-\frac{1x}{5}-\frac{4}{5})}[/tex]
solve the above equation:
[tex]\to f^{-1}(x)= \frac{-x-4}{5}\\\\\to f^{-1}(x)= -\frac{x+4}{5}\\[/tex]
Let
[tex]y= f^{-1} x= -(\frac{x+4}{5})\\\\[/tex]
inverse the above function:
[tex]\to x= -(\frac{y+4}{5})\\\\\to 5x= -(y+4)\\\\\to 5x= -y-4\\\\\to\boxed {y=-5x-4}\\\\[/tex]
