Find the domain of the function f\left(x\right)=\frac{1}{3x+8}
 
. What is the only value of 
 not in the domain?

Only Value


To find the domain of the function \( f(x) = \frac{1}{3x + 8} \), we need to identify the values of \( x \) for which the function is undefined. The function will be undefined when the denominator equals zero because division by zero is not possible.

### Step 1: Find the value where the denominator is zero
Set the denominator equal to zero and solve for \( x \):
\[
3x + 8 = 0
\]

### Step 2: Solve for \( x \)
\[
3x = -8
\]
\[
x = -\frac{8}{3}
\]

### Step 3: Determine the domain
The function is defined for all real values of \( x \) except \( x = -\frac{8}{3} \).

### Final Answer:
**The only value not in the domain is** \( x = -\frac{8}{3} \).

Would you like to see more details or have any questions?

Here are 5 related questions that expand on this topic:
1. How do you find the domain of functions with square roots?
2. What is the domain of the function \( g(x) = \sqrt{3x+8} \)?
3. How does the domain change for functions like \( f(x) = \frac{1}{(3x+8)^2} \)?
4. What happens to the domain if the function is \( f(x) = \ln(3x+8) \)?
5. How do you determine the range of the function \( f(x) = \frac{1}{3x+8} \)?

**Tip**: When finding the domain of rational functions, always start by identifying values that make the denominator zero, as these are the points where the function is undefined.

Find the domain of the function f(x) = 1/(3x + 8). What is the only value not in the domain?

Learn how to find the domain of the rational function f(x) = 1/(3x + 8). This problem helps students identify values that make the denominator zero and understand the concept of undefined points in functions. Suitable for students in Grades 9-10.

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