https://file.aiquickdraw.com/mathbot/file/17270809222238hw8xinm.jpg

The problem in the image can be translated as follows:

"If \( g(x) = x^2 + 4 \) with \( x \geq 0 \), then the value of \( g^{-1}(13) \) is..."

### Solution:

1. The function \( g(x) = x^2 + 4 \) is given, and we are asked to find \( g^{-1}(13) \).
   
2. The inverse function, \( g^{-1}(y) \), will return the value of \( x \) such that \( g(x) = y \).

3. Set \( g(x) = 13 \):
   \[
   x^2 + 4 = 13
   \]
   Subtract 4 from both sides:
   \[
   x^2 = 9
   \]
   Taking the square root of both sides, we get:
   \[
   x = \sqrt{9} = 3
   \]

   Since the condition \( x \geq 0 \) is given, we discard the negative root.

### Therefore, the value of \( g^{-1}(13) \) is \( \boxed{3} \).

Would you like further explanation or have any other questions?

Here are five related questions to explore this concept further:
1. How do you determine the domain of an inverse function?
2. What is the significance of the condition \( x \geq 0 \) in this problem?
3. How would you graph both \( g(x) \) and \( g^{-1}(x) \) on the same plane?
4. What would change if the function were \( g(x) = x^2 + 1 \) instead of \( x^2 + 4 \)?
5. How do you find the inverse of a general quadratic function?

**Tip:** When finding the inverse of a function, always make sure that the function is one-to-one (or restricted) over the given domain, so that an inverse exists.

Jika g(x) = x^2 + 4 dengan x ≥ 0, maka nilai dari g^(-1)(13) adalah...

Learn how to find the inverse of the function g(x) = x^2 + 4 when x is greater than or equal to zero. This problem involves understanding inverse functions and solving quadratic equations. The solution demonstrates key algebraic techniques and is suitable for students in Grades 9-12.

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