Question

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

Answer 1

Answer:

(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