Respuesta :

Nerdgirl23
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.

A function assigns the values. The inverse of the function f(x) is g(x), which is equal to 4x+48.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The inverse of the given function can be found as shown below.

Step1: Rewrite the equation in the form of y and x.

f(x)=(1/4)x-12

y=(1/4)x-12

Step2: solve the above-formed equation for x,

y=(1/4)x-12

y +12 = (1/4)x

4(y+12) = x

Step 3: replace x with y, and y with x.

4(x+12) = y

4x + 48 = y

Therefore, the inverse of the function f(x) is g(x), which is equal to 4x+48.

Learn more about Function:

https://brainly.com/question/5245372

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