Find the inverse of the linear function y=1/2x+3.

2 (x-3) = y

Step-by-step explanation:

y = 1/2 x + 3

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

Exchange x and y

x = 1/2y + 3

Then solve for 3

Subtract 3 from each side

x-3 = 1/2 y - 3+3

x-3 = 1/2 y

Multiply each side by 2

2 (x-3) = 1/2 * 2 y

2 (x-3) = y

This is the inverse

Interchange the variables:

x = 1/2y + 3

Solve for y:

Subtract 3 from each side:

x-3 = 1/2y

Multiply both sides by 2:

2x-6 = y

Rewrite the equation with y on the left side:

y = 2x-6

Replace y with f^-1 (x):

f^-1 (x) = 2x-6