Answer:
B. f -1(x) = x + 2 / 5
[tex]f^{-1}(x)=\frac{x+2}{5}[/tex]
Step-by-step explanation:
To find the inverse of a function we need to interchange x and y an solve for y.
Since [tex]f(x)=y[/tex], then
[tex]f(x)=5x-2[/tex]
[tex]y=5x-2[/tex]
[tex]x=5y-2[/tex]
Add 2 to both sides
[tex]x+2=5y-2+2[/tex]
[tex]x+2=5y[/tex]
Divide both sides by 5
[tex]\frac{x+2}{5}=\frac{5y}{5}[/tex]
[tex]\frac{x+2}{5}=y[/tex]
[tex]y=\frac{x+2}{5}[/tex]
[tex]f^{-1}(x)=\frac{x+2}{5}[/tex]
We can conclude that the correct answer is B. f -1(x) = x + 2 / 5
