https://file.aiquickdraw.com/mathbot/file/1725466295956yq3xqgq0.jpg

The image contains the following problem:

Given the functions:
\[
F(x) = x^2 + 1
\]
\[
g(x) = \frac{1}{x}
\]

You are asked to evaluate \( F(g(4)) \).

### Solution:

1. First, find \( g(4) \):
   \[
   g(4) = \frac{1}{4}
   \]

2. Next, substitute \( g(4) \) into \( F(x) \) to find \( F(g(4)) \):
   \[
   F\left(\frac{1}{4}\right) = \left(\frac{1}{4}\right)^2 + 1
   \]

3. Calculate:
   \[
   \left(\frac{1}{4}\right)^2 = \frac{1}{16}
   \]
   \[
   F\left(\frac{1}{4}\right) = \frac{1}{16} + 1 = \frac{1}{16} + \frac{16}{16} = \frac{17}{16}
   \]

Thus, the value of \( F(g(4)) \) is \(\frac{17}{16}\).

Would you like more details on any of these steps or have any other questions?

### Related Questions:
1. What is the general process for evaluating a composite function?
2. How would the result change if \( g(x) = x + 1 \)?
3. Can you find \( F(g(-2)) \) using the given functions?
4. How do we interpret composite functions in real-life scenarios?
5. What are the domain restrictions for the function \( g(x) = \frac{1}{x} \)?

### Tip:
When working with composite functions, always evaluate the innermost function first before applying the outer function.

Consider the functions F(x) = x^2 + 1 and g(x) = 1/x. Evaluate F(g(4)).

Learn how to evaluate composite functions with given functions F(x) = x^2 + 1 and g(x) = 1/x. This problem involves finding F(g(4)), highlighting key algebraic concepts and composite function evaluation. Suitable for students in Grades 9-11.

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