Inverse function for f (x) = square root 2x-6

(x^2 + 6) / 2

or 1/2 x^2 + 3

Step-by-step explanation:

f (x) = sqrt (2x-6)

y = sqrt (2x-6)

To find the inverse function, we interchange the x and y and solve for y

x = sqrt (2y-6)

Square each side

x^2 = sqrt (2y-6) ^2

x^2 = 2y-6

Add 6 to each to each side

x^2 + 6 = 2y-6+6

x^2 + 6 = 2y

Divide each side by 2

(x^2 + 6) / 2 = 2y/2

(x^2 + 6) / 2 = y

The inverse function is

(x^2 + 6) / 2

or 1/2 x^2 + 3