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f(x) = x โ€“ 2. Find the inverse of f(x).A.๐‘“โˆ’1(๐‘ฅ)=๐‘ฅโˆ’2f โˆ’1 (x)=xโˆ’2B.๐‘“โˆ’1(๐‘ฅ)=2๐‘ฅf โˆ’1 (x)=2xC.๐‘“โˆ’1(๐‘ฅ)=๐‘ฅ+2f โˆ’1 (x)=x+2D.๐‘“โˆ’1(๐‘ฅ)=2โˆ’๐‘ฅf โˆ’1 (x)=2โˆ’x

Question

f(x) = x โ€“ 2. Find the inverse of f(x).

A. ๐‘“^{-1}(๐‘ฅ)=๐‘ฅโˆ’2
f^{-1}(x) = x - 2

B. ๐‘“^{-1}(๐‘ฅ)=2๐‘ฅ
f^{-1}(x) = 2x

C. ๐‘“^{-1}(๐‘ฅ)=๐‘ฅ+2
f^{-1}(x) = x + 2

D. ๐‘“^{-1}(๐‘ฅ)=2โˆ’๐‘ฅ
f^{-1}(x) = 2 - x

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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:

  1. Replace f(x) with y, so the equation becomes y = x - 2.
  2. Swap x and y to get x = y - 2.
  3. 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. ๐‘“โˆ’1(๐‘ฅ)=๐‘ฅ+2.

This problem has been solved

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f(x) = x โ€“ 2. Find the inverse of f(x).A.๐‘“โˆ’1(๐‘ฅ)=๐‘ฅโˆ’2f โˆ’1 (x)=xโˆ’2B.๐‘“โˆ’1(๐‘ฅ)=2๐‘ฅf โˆ’1 (x)=2xC.๐‘“โˆ’1(๐‘ฅ)=๐‘ฅ+2f โˆ’1 (x)=x+2D.๐‘“โˆ’1(๐‘ฅ)=2โˆ’๐‘ฅf โˆ’1 (x)=2โˆ’x

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