To take the inverse of a function, you switch x and y. Y = (1/4)X-12, so for the inverse X = (1/4)Y-12. Then you solve for Y. X + 12 = (1/4)Y. 4X + 48 = Y. Therefore the inverse of y=(1/4)x-12 is y=4x+48. To check, you can plug in a point. The original function has the point (4, -11), so the inverse should have the point (-11, 4). It does. 4 * -11 is -44, add 48 to that to get 4.