Question

Find the error & explain why it is wrong: laural had to find the inverse of the function f(x)=-x+3. What did she do wrong? State the inverse by replacing y with f^-1(x). Step___is incorrect because __________________. Instead, you should ____________________.

A. Step A: f(x)=-x+3
B. Step B: y=-x+3
C. Step C: -x=y+3
D. Step D: -3-x=y
E. Step E: f^-1(x)=-3-x

Answer 1

The error in finding the inverse of the function f(x) = -x + 3 occurs in Step E: f^-1(x) = -3 - x. The correct steps to find the inverse are explained and the correct inverse function is f^-1(x) = -x + 3.

Step-by-step explanation:

The error in finding the inverse of the function f(x) = -x + 3 occurs in Step E: f^-1(x)=-3-x.

The correct steps to find the inverse are as follows:

• Step A: Start with the original function, f(x)=-x+3.
• Step B: Replace f(x) with y, so we have the equation y = -x + 3.
• Step C: Swap x and y to get x = -y + 3.
• Step D: Isolate y by subtracting 3 from both sides, which gives y = -x + 3.

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