Question

let $f(x) = 5x + 3$
$f^{-1}(x) = $
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Explanation:

Step1: Let \( y = f(x) \)

We start by setting \( y = 5x + 3 \). This is the original function, and we want to find its inverse, so we'll solve for \( x \) in terms of \( y \).

Step2: Solve for \( x \)

First, subtract 3 from both sides of the equation:
\( y - 3 = 5x \)
Then, divide both sides by 5:
\( x=\frac{y - 3}{5} \)

Step3: Replace \( x \) with \( f^{-1}(x) \) and \( y \) with \( x \)

The inverse function \( f^{-1}(x) \) is obtained by replacing \( y \) with \( x \) in the expression we found for \( x \). So we get:
\( f^{-1}(x)=\frac{x - 3}{5} \)

Answer:

\( \frac{x - 3}{5} \)