Find the inverse function in slope-intercept form (mx+b):
f, of, x, equals, one third, x, plus, 15
f(x)=
3
1
​
 x+15

To find the inverse of the function \( f(x) = \frac{1}{3}x + 15 \), we will follow these steps:

1. **Replace** \( f(x) \) with \( y \):
   \[
   y = \frac{1}{3}x + 15
   \]

2. **Swap** \( x \) and \( y \) to find the inverse:
   \[
   x = \frac{1}{3}y + 15
   \]

3. **Solve for** \( y \) to express it in terms of \( x \):

   - Subtract 15 from both sides:
     \[
     x - 15 = \frac{1}{3}y
     \]

   - Multiply both sides by 3 to isolate \( y \):
     \[
     3(x - 15) = y
     \]

   - Simplify the equation:
     \[
     y = 3x - 45
     \]

4. **Rewrite** the inverse function in slope-intercept form \( y = mx + b \):

   The inverse function is:
   \[
   f^{-1}(x) = 3x - 45
   \]

### The Inverse Function:
\[
f^{-1}(x) = 3x - 45
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you find the inverse of a function algebraically?
2. What is the domain and range of the inverse function?
3. How do you verify that two functions are inverses of each other?
4. Can you explain the concept of one-to-one functions and their inverses?
5. How does the graph of a function compare to the graph of its inverse?

#### Tip:
When finding the inverse of a function, always ensure that the original function is one-to-one (passes the horizontal line test), as only one-to-one functions have inverses that are also functions.

Find the inverse function in slope-intercept form (mx+b): f(x) = 1/3x + 15

Learn how to find the inverse function for f(x) = 1/3x + 15 in slope-intercept form. This solution covers key algebraic concepts, including inverse functions and slope-intercept form. Suitable for students in Grades 9-11.

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