Questions: Find the inverse function of (f). [f(x)=9x+5]

Transcript text: Submit Answer [0/1 Points] DETAILS Find the inverse function of $f$. \[ f(x)=9 x+5 \]

Solution

Solution Steps

To find the inverse of a function, we need to solve for $ x $ in terms of $ y $ where $ y = f(x) $. For the given function $ f(x) = 9x + 5 $, we will set $ y = 9x + 5 $ and solve for $ x $ in terms of $ y $. The resulting expression will be the inverse function $ f^{-1}(y) $.

Step 1: Set Up the Equation

We start with the function $ f(x) = 9x + 5 $. To find the inverse function, we set $ y = f(x) $, which gives us the equation: \[ y = 9x + 5 \]

Step 2: Solve for $ x $

Next, we rearrange the equation to solve for $ x $: \[ y - 5 = 9x \] \[ x = \frac{y - 5}{9} \]

Step 3: Express the Inverse Function

The inverse function $ f^{-1}(y) $ can be expressed as: \[ f^{-1}(y) = \frac{y - 5}{9} \] To express it in terms of $ x $, we replace $ y $ with $ x $: \[ f^{-1}(x) = \frac{x - 5}{9} \]