Find the inverse function in slope-intercept form (mx+b):
f(x)=5x+10

To find the inverse of the function \( f(x) = 5x + 10 \), follow these steps:

### Step 1: Replace \( f(x) \) with \( y \)
\[
y = 5x + 10
\]

### Step 2: Swap \( x \) and \( y \)
\[
x = 5y + 10
\]

### Step 3: Solve for \( y \)
First, subtract 10 from both sides:
\[
x - 10 = 5y
\]
Next, divide both sides by 5:
\[
y = \frac{x - 10}{5}
\]

### Step 4: Replace \( y \) with \( f^{-1}(x) \)
\[
f^{-1}(x) = \frac{x - 10}{5}
\]

So, the inverse function is:
\[
f^{-1}(x) = \frac{1}{5}x - 2
\]

This is in slope-intercept form, where \( m = \frac{1}{5} \) and \( b = -2 \).

Would you like more details on any step?

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Here are 5 related questions to expand your understanding:
1. How do you verify if two functions are inverses of each other?
2. What happens if the original function has a slope of zero?
3. Can every function have an inverse? Why or why not?
4. How does the inverse function relate to the graph of the original function?
5. What are the domain and range of the inverse function?

**Tip:** For a function to have an inverse, it must be one-to-one, meaning it passes the horizontal line test.

Find the inverse function in slope-intercept form (mx+b): f(x)=5x+10

Learn how to find the inverse function of f(x) = 5x + 10 in slope-intercept form. This problem involves key algebraic concepts such as linear equations and inverse functions. Suitable for high school students in Grades 9-12.

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