Questions: Find the inverse. f(x) = 1/5 x + (3/5)

Find the inverse. f(x) = 1/5 x + (3/5)
Transcript text: $\begin{array}{l}\text { Find the inverse. } \\ f(x)=\frac{1}{5} x+\left(\frac{3}{5}\right)\end{array}$
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Solution

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Solution Steps

Step 1: Replace \( f(x) \) with \( y \)

Start by rewriting the function \( f(x) \) as \( y \): \[ y = \frac{1}{5}x + \frac{3}{5} \]

Step 2: Swap \( x \) and \( y \)

To find the inverse, swap \( x \) and \( y \): \[ x = \frac{1}{5}y + \frac{3}{5} \]

Step 3: Solve for \( y \)

Isolate \( y \) by performing the following steps:

  1. Subtract \( \frac{3}{5} \) from both sides: \[ x - \frac{3}{5} = \frac{1}{5}y \]
  2. Multiply both sides by 5 to eliminate the fraction: \[ 5\left(x - \frac{3}{5}\right) = y \]
  3. Simplify the equation: \[ y = 5x - 3 \]

The inverse function is \( f^{-1}(x) = 5x - 3 \).

Final Answer

\(\boxed{f^{-1}(x) = 5x - 3}\)

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