se algebra to find the inverse of the given one-to-one function.
f (x) = 5x + 3

To find the inverse of the function \( f(x) = 5x + 3 \) using algebra, follow these steps:

1. **Replace** \( f(x) \) with \( y \):
   \[
   y = 5x + 3
   \]

2. **Interchange** \( x \) and \( y \) (this step represents swapping the input and output of the function):
   \[
   x = 5y + 3
   \]

3. **Solve for** \( y \):
   \[
   x - 3 = 5y
   \]
   \[
   y = \frac{x - 3}{5}
   \]

4. The inverse function is:
   \[
   f^{-1}(x) = \frac{x - 3}{5}
   \]

Thus, the inverse of \( f(x) = 5x + 3 \) is \( f^{-1}(x) = \frac{x - 3}{5} \).

Would you like more details or have any questions? Here are some related questions to explore:

1. How do you verify if a function is one-to-one?
2. How do you check if the inverse of a function is correct?
3. What are the properties of inverse functions?
4. How do you find the inverse of a quadratic function?
5. Can all functions have inverses?

**Tip:** To check if two functions are inverses, compose them: \( f(f^{-1}(x)) = f^{-1}(f(x)) = x \).

Use algebra to find the inverse of the given one-to-one function. f(x) = 5x + 3

Learn how to find the inverse of the one-to-one function f(x) = 5x + 3 using algebra. This step-by-step guide covers essential algebraic concepts, including inverse functions and solving linear equations. Suitable for high school students in Grades 9-12.

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