f(x) = x – 2. Find the inverse of f(x).A.𝑓−1(𝑥)=𝑥−2f −1 (x)=x−2B.𝑓−1(𝑥)=2𝑥f −1 (x)=2xC.𝑓−1(𝑥)=𝑥+2f −1 (x)=x+2D.𝑓−1(𝑥)=2−𝑥f −1 (x)=2−x
Question
f(x) = x – 2. Find the inverse of f(x).
A. 𝑓^{-1}(𝑥)=𝑥−2
f^{-1}(x) = x - 2
B. 𝑓^{-1}(𝑥)=2𝑥
f^{-1}(x) = 2x
C. 𝑓^{-1}(𝑥)=𝑥+2
f^{-1}(x) = x + 2
D. 𝑓^{-1}(𝑥)=2−𝑥
f^{-1}(x) = 2 - x
Solution
The inverse of a function is found by switching the x and y (or f(x)) and solving for y.
Here's how you can find the inverse of the function f(x) = x - 2:
- Replace f(x) with y, so the equation becomes y = x - 2.
- Swap x and y to get x = y - 2.
- Solve the equation for y to find the inverse function. Add 2 to both sides of the equation to isolate y, which gives you y = x + 2.
So, the inverse of the function f(x) = x - 2 is f^-1(x) = x + 2.
Therefore, the correct answer is C. 𝑓−1(𝑥)=𝑥+2.
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