What is the domain of $f(x)=\frac{1}{x}$ ? What is its range?

Step 1 ：The domain of a function is the set of all possible input values (often the 'x' variable), which produce a valid output from a particular function. The range of a function is the possible values of the output, or dependent variable.

Step 2 ：For the function \(f(x)=\frac{1}{x}\), the domain is all real numbers except 0, because we cannot divide by zero.

Step 3 ：The range is also all real numbers except 0, because the function will never output a value of 0.

Step 4 ：The domain of \(f(x)=\frac{1}{x}\) is all real numbers except 0, and its range is also all real numbers except 0. In mathematical notation, this can be written as:

Step 5 ：Domain: \(x \in \mathbb{R} \setminus \{0\}\)

Step 6 ：Range: \(f(x) \in \mathbb{R} \setminus \{0\}\)

Step 7 ：\(\boxed{\text{Domain: } x \in \mathbb{R} \setminus \{0\}, \text{ Range: } f(x) \in \mathbb{R} \setminus \{0\}}\)