Question

Given h(x) = 3/5)x + 2, find the inverse of the linear function.

Answer 1

To find the inverse of the linear function h(x), swap x and y in the equation, solve for y, and then express the new function in terms of x. The inverse function is h⁻¹(x) = (5/3)(x - 2).

Step-by-step explanation:

To find the inverse of the linear function h(x) = (3/5)x + 2, we need to switch the roles of x and y, and then solve for y to get the new function x.

1. Let y = h(x), which gives us y = (3/5)x + 2.
2. Swap x and y to get x = (3/5)y + 2.
3. Solve for y by subtracting 2 from both sides to get x - 2 = (3/5)y.
4. Multiply both sides by 5/3 to isolate y, which gives us (5/3)(x - 2) = y.
5. Finally, the inverse function is h-1(x) = (5/3)(x - 2).