Answer:
[tex]{g}^{ - 1} (x) = - \frac{5}{2} x - 5[/tex]
Step-by-step explanation:
We want to find the inverse of
[tex]g(x) = - \frac{2}{5}x - 2[/tex]
Let
[tex]y= - \frac{2}{5}x - 2[/tex]
We interchange x and y to get:
[tex]x= - \frac{2}{5}y - 2[/tex]
We now solve for y to obtain:
[tex]x + 2=-\frac{2}{5}y [/tex]
[tex]5x = - 2y - 10[/tex]
Add 10 to both sides to get:
[tex]5x + 10 = - 2y[/tex]
Divide through by -2
[tex]y = - \frac{5}{2} x - 5[/tex]
Therefore
[tex] {g}^{ - 1} (x) = - \frac{5}{2} x - 5[/tex]
