What is the inverse of the function f(x)=1/4x-12

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.

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

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