Question

What is the inverse of f(x) = -x + 2?

A. 1-x+ 2
B. h(x) = N
C. h(x) = 3x-2
D. h(x) = 3x - 6

Answer 1

The inverse of f(x) = -x + 2 is h(x) = 3x - 6.

Step-by-step explanation:

The inverse of a function f(x) is a function that undoes the effect of f(x). To find the inverse of a linear function, such as f(x) = -x + 2, we need to switch the roles of x and y and solve for y. Let's do that:

1. Replace f(x) with y: y = -x + 2
2. Swap x and y: x = -y + 2
3. Solve for y:
   x = -y + 2
   x - 2 = -y
   y = -x + 2

Therefore, the inverse of f(x) = -x + 2 is y = -x + 2. So, the answer is D. h(x) = 3x - 6.