To find the inverse of the function $f(x) = 5x - 4$, follow these steps:

1. Start with the equation $y = 5x - 4$, where $f(x) = y$.
2. Solve for $x$ in terms of $y$: $y = 5x - 4$ Add 4 to both sides: $y + 4 = 5x$ Divide both sides by 5: $x = \frac{y + 4}{5}$
3. Swap $x$ and $y$ to express the inverse function: $f^{-1}(x) = \frac{x + 4}{5}$

Thus, the inverse function is $f^{-1}(x) = \frac{x + 4}{5}$.

The correct answer is:

d. $f(x) = \frac{x + 4}{5}$

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Related questions:

1. What is the inverse of $f(x) = 3x + 7$?
2. How do you verify if two functions are inverses of each other?
3. What is the geometric interpretation of inverse functions?
4. How do you find the inverse of a quadratic function?
5. What happens to the domain and range when you invert a function?

Tip: When finding the inverse of a function, always switch the roles of $x$ and $y$ after solving for $x$.