It seems like there is a part of the question missing, specifically the definition of the function $f(x)$. To determine the domain and range of $f(x)$, I need to know the actual expression or form of the function.

Could you please provide the complete function definition for $f(x)$? Once you provide that, I can help you find the domain and range.

In the meantime, here are some common scenarios:

1. For a linear function $f(x) = mx + b$:

   • Domain: All real numbers ($-\infty, \infty$)
   • Range: All real numbers ($-\infty, \infty$)

2. For a quadratic function $f(x) = ax^2 + bx + c$:

   • Domain: All real numbers ($-\infty, \infty$)
   • Range: Depending on $a$, it could be $[k, \infty)$ or $(-\infty, k]$, where $k$ is the vertex's y-coordinate.

3. For a square root function $f(x) = \sqrt{x}$:

   • Domain: $[0, \infty)$
   • Range: $[0, \infty)$

4. For a reciprocal function $f(x) = \frac{1}{x}$:

   • Domain: All real numbers except $x = 0$ ($x \neq 0$)
   • Range: All real numbers except $y = 0$ ($y \neq 0$)

5. For an exponential function $f(x) = a^x$:

   • Domain: All real numbers ($-\infty, \infty$)
   • Range: $(0, \infty)$ if $a > 1$.

Please provide the specific form of $f(x)$ so I can give a precise answer regarding its domain and range.

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Follow-Up Questions

1. What is the specific function $f(x)$ that you're working with?
2. Are there any restrictions on $x$ that we need to consider for this function?
3. Does the function involve any absolute values or piecewise definitions?
4. Are there any vertical or horizontal asymptotes we need to consider?
5. Are you dealing with any real-world constraints that might affect the domain or range?

Tip

Always check for restrictions like division by zero or negative values under a square root when determining the domain of a function.