f(x) = (<square root>x + 1)/<square root>x + 2;  x = 4

You are given the function \( f(x) = \frac{\sqrt{x} + 1}{\sqrt{x} + 2} \), and you need to evaluate it at \( x = 4 \).

### Steps:
1. First, substitute \( x = 4 \) into the function.
   \[
   f(4) = \frac{\sqrt{4} + 1}{\sqrt{4} + 2}
   \]
2. The square root of 4 is 2, so:
   \[
   f(4) = \frac{2 + 1}{2 + 2} = \frac{3}{4}
   \]

Thus, \( f(4) = \frac{3}{4} \).

Would you like more details on the steps or clarifications?

Here are some follow-up questions you might find interesting:
1. How would you evaluate \( f(x) \) if \( x = 9 \)?
2. What happens to \( f(x) \) as \( x \) approaches infinity?
3. How would you differentiate \( f(x) \) with respect to \( x \)?
4. Can you simplify the function for any particular value of \( x \)?
5. What are the domain and range of \( f(x) \)?

**Tip:** When substituting values, always calculate the inner expressions (like square roots) first to simplify the process.

Learn how to evaluate the function f(x) = (√x + 1)/(√x + 2) when x = 4. This solution includes a step-by-step guide for working with square roots and functions, suitable for students in Grades 7-9.

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