Find the Inverse function f^-1 (x) for the given function f (x) = 2/5x-2

f^-1 (x) = 5/2 x + 5

Step-by-step explanation:

To find the inverse function, exchange x and y and solve for y

y = 2/5 x - 2

Exchange x and y

x = 2/5 y - 2

Solve for y

Add 2 to each side

x+2 = 2/5y-2+2

x+2 = 2/5 y

Multiply by 5/2 to isolate y

5/2 (x+2) = 2/5 y * 5/2

5/2 (x+2) = y

5/2 x + 5 = y