Question

Find the inverse of the function:

f(x) = -x +4
A f -1(x) = -4x + 16
B f -1(x) = - 3x + 2
C f -1(x) = 40 + 16
D f-1(x) = 1/2 +1

Answer 1

The correct inverse of the function f(x) = -x + 4 is f-1(x) = 4 - x, which corresponds to option B f-1(x) = - 3x + 2.

Step-by-step explanation:

To find the inverse of the function f(x) = -x + 4, we need to switch the places of x and f(x), then solve for the new x. Here are the steps:

• Replace the function notation f(x) with y: y = -x + 4.
• Switch x and y: x = -y + 4.
• Solve for y: Add y to both sides to get x + y = 4 then subtract x from both sides to get y = 4 - x. The function notation for the inverse is typically f-1(x) so we write f-1(x) = 4 - x.

Therefore, the correct inverse function is B f-1(x) = - 3x + 2.