find the inverse functiona; 1.) f(x)=3x+6  

To find the inverse of the function \( f(x) = 3x + 6 \), follow these steps:

### Step 1: Replace \( f(x) \) with \( y \)
\[
y = 3x + 6
\]

### Step 2: Swap \( x \) and \( y \)
The inverse of a function is found by switching \( x \) and \( y \). This gives:
\[
x = 3y + 6
\]

### Step 3: Solve for \( y \)
Isolate \( y \) to get the inverse function:
\[
x - 6 = 3y
\]
\[
y = \frac{x - 6}{3}
\]

### Step 4: Write the inverse function
The inverse function is:
\[
f^{-1}(x) = \frac{x - 6}{3}
\]

Let me know if you would like more details or if you have any questions!

Here are 5 related questions to further explore:
1. What is the domain and range of \( f(x) = 3x + 6 \)?
2. How do you verify that two functions are inverses of each other?
3. How does the graph of a function compare to the graph of its inverse?
4. What happens to the slope when you find the inverse of a linear function?
5. Can every function have an inverse?

**Tip**: Always check that a function is one-to-one before finding its inverse, as only one-to-one functions have inverses.

find the inverse function; 1.) f(x) = 3x + 6

Learn how to find the inverse of the linear function f(x) = 3x + 6. This step-by-step solution covers key algebraic concepts, including how to solve for the inverse function. Suitable for students in Grades 9-11.

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