Question

What is the inverse function of f(x) =
x - 2
f- (x)=
x -2
f-'(x) =
2x
x -1
f-1(x)=
2x x+1
f-(x)=-=
2x x -1

Answer 1

To find the inverse function of \( f(x) = x - 2 \), we need to follow a few steps. Let's clarify that first.

1. **Start with the function**: \( y = f(x) = x - 2 \).
2. **Swap \( x \) and \( y \)**: \( x = y - 2 \).
3. **Solve for \( y \)**: Add 2 to both sides, so \( y = x + 2 \).

Therefore, the inverse function is:
\[
f^{-1}(x) = x + 2
\]

Now that we have \( f^{-1}(x) \), let's check your other forms of inverse functions:

- \( f^{-1}(x) = 2x \) and \( f^{-1}(x) = 2x + 1 \) and \( f^{-1}(x) = 2x - 1 \) are incorrect based on the original function.

The correct inverse of \( f(x) = x - 2 \) is:
\[
f^{-1}(x) = x + 2
\]

If you have any specific functions or transformations you would like clarification on, let me know!