f(x) = x โ 2. Find the inverse of f(x).A.๐โ1(๐ฅ)=๐ฅโ2f โ1 (x)=xโ2B.๐โ1(๐ฅ)=2๐ฅf โ1 (x)=2xC.๐โ1(๐ฅ)=๐ฅ+2f โ1 (x)=x+2D.๐โ1(๐ฅ)=2โ๐ฅf โ1 (x)=2โx
Question
f(x) = x โ 2. Find the inverse of f(x).A.๐โ1(๐ฅ)=๐ฅโ2f โ1 (x)=xโ2B.๐โ1(๐ฅ)=2๐ฅf โ1 (x)=2xC.๐โ1(๐ฅ)=๐ฅ+2f โ1 (x)=x+2D.๐โ1(๐ฅ)=2โ๐ฅf โ1 (x)=2โx
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. ๐โ1(๐ฅ)=๐ฅ+2.
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