Answer:
[tex]\huge\boxed{\sf f^{-1}(x)=5x+10}[/tex]
Step-by-step explanation:
Given function:
[tex]\displaystyle f(x)=\frac{x}{5} -2[/tex]
Put f(x) = y
[tex]\displaystyle y=\frac{x}{5} -2[/tex]
Swap x and y
[tex]\displaystyle x = \frac{y}{5} -2[/tex]
Now, solve for y
[tex]\displaystyle x = \frac{y}{5} -2[/tex]
Add 2 to both sides
[tex]\displaystyle x + 2 =\frac{y}{5}[/tex]
Multiply 5 to both sides
[tex]5(x+2)=y[/tex]
Distribute
[tex]5x + 10 =y[/tex]
Put y = f⁻¹(x)
[tex]\boxed{f^{-1}(x)=5x+10}[/tex]
[tex]\rule[225]{225}{2}[/tex]
