Answer:
[tex]y=5x+10[/tex]
Step-by-step explanation:
[tex]f(x)=\frac{x}{5} -2[/tex]
To find the inverse of the function we do the following steps
Replace f(x) with y
[tex]y=\frac{x}{5} -2[/tex]
Replace y with x and x with y
[tex]x=\frac{y}{5} -2[/tex]
Solve the equation for y
Add 2 on both sides
[tex]x+2=\frac{y}{5}[/tex]
Now multiply by 5 on both sides
[tex]5(x+2)=y[/tex]
Now distribute 5 inside the parenthesis
[tex]5x+10= y[/tex]
[tex]y=5x+10[/tex]
