Questions: Question 10 of 10 f(x)=x-3. Find the inverse of f(x). A. f^-1(x)=x+3 B. f^-1(x)=3-x C. f^-1(x)=3x D. f^-1(x)=x-3

Transcript text: Question 10 of 10 $f(x)=x-3$. Find the inverse of $f(x)$. A. $f^{-1}(x)=x+3$ B. $f^{-1}(x)=3-x$ C. $f^{-1}(x)=3 x$ D. $f^{-1}(x)=x-3$

Solution

Solution Steps

To find the inverse of the function $ f(x) = x - 3 $, we need to solve for $ x $ in terms of $ y $ where $ y = f(x) $. This involves swapping $ x $ and $ y $ and then solving for $ y $.

Step 1: Define the Function

Given the function $ f(x) = x - 3 $.

Step 2: Set Up the Equation for the Inverse

To find the inverse, we set $ y = f(x) $. Therefore, we have: \[ y = x - 3 \]

Step 3: Solve for $ x $ in Terms of $ y $

Rearrange the equation to solve for $ x $: \[ y = x - 3 \] \[ x = y + 3 \]

Step 4: Express the Inverse Function

The inverse function $ f^{-1}(x) $ is obtained by swapping $ x $ and $ y $: \[ f^{-1}(x) = x + 3 \]