Question

f(x) =1/x.x -9 find domain and range

Answer 1

To find the domain and range of the function \( f(x) = \frac{1}{x} \cdot x - 9 \), first, let's simplify the function.

1. **Simplifying the function**:
\[
f(x) = \frac{1}{x} \cdot x - 9 = 1 - 9 = -8
\]
The function simplifies to a constant value of \( -8 \) for any \( x \neq 0 \).

2. **Finding the Domain**:
The domain of a function includes all the values of \( x \) for which the function is defined. In this case, the function \( f(x) \) is undefined when \( x = 0 \) because division by zero is not allowed. Therefore, the domain is all real numbers except for 0:
\[
\text{Domain: } (-\infty, 0) \cup (0, \infty)
\]

3. **Finding the Range**:
The range of a function is the set of possible output values. Since \( f(x) \) simplifies to the constant value of \(-8\) for all \( x \) in the domain, the range is :
\[
\text{Range: } \{-8\}
\]

To summarize:
- **Domain**: \( (-\infty, 0) \cup (0, \infty) \)
- **Range**: \( \{-8\} \)