Which of the is the inverse of (\f(x) = 5x - 4\)?

Question 11Select one:

a.
(\f(x) = (x - 4)/5\)


b.
(\f(x) = (4 - x)/5\)


c.
(\f(x) = 1/(5x - 4)\)


d.
(\f(x) = (x + 4)/5\)

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 \( x \).

Which of the is the inverse of (f(x) = 5x - 4)?

Question 11Select one:

a. (f(x) = (x - 4)/5)

b. (f(x) = (4 - x)/5)

c. (f(x) = 1/(5x - 4))

d. (f(x) = (x + 4)/5)

Learn how to find the inverse of the function f(x) = 5x - 4 with a step-by-step explanation. This algebra problem explains the process of solving for the inverse function using the formula and inverse function theorem. Suitable for high school students in Grades 9-12.

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