Question

What’s the inverse of the linear function h(x)= 4/5x+1?
Why is it not 5x-5/4? What would it be?

Answer 1

The inverse of the linear function h(x) = (4/5)x + 1 is found by swapping x and y and then solving for y, resulting in y = (5/4)(x - 1). It is not 5x - 5/4 because this does not reverse the operations of h(x) correctly.

Step-by-step explanation:

The question at hand is about finding the inverse of a linear function. Specifically, we want to find the inverse of the function h(x) = (4/5)x + 1. To find the inverse, we need to solve for x by following these steps:

1. Let y = (4/5)x + 1.
2. Swap x and y to get x = (4/5)y + 1.
3. Solve for y by isolating it on one side of the equation: y = (5/4)(x - 1).

It is incorrect to state that the inverse is 5x - 5/4 because this does not adhere to the procedural steps of finding an inverse function, and it does not correctly reverse the operations of the original function. The correct inverse function for h(x) is y = (5/4)(x - 1).