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

The question in the image asks:

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

### Solution:

We need to find the inverse of \( g(x) = x^2 + 4 \), meaning \( g^{-1}(y) \) will give us the value of \( x \) such that \( g(x) = y \).

#### Step 1: Set \( g(x) = 13 \)
\[
x^2 + 4 = 13
\]

#### Step 2: Solve for \( x \)
\[
x^2 = 13 - 4 = 9
\]
\[
x = \sqrt{9} = 3
\]

Since \( x \geq 0 \) by the given condition, the solution is \( x = 3 \).

Thus, \( g^{-1}(13) = 3 \).

Would you like a detailed explanation of how the inverse function works? 

### Related questions:
1. What is the general formula for finding the inverse of a quadratic function?
2. If \( g(x) = x^2 + 1 \), what is \( g^{-1}(10) \)?
3. How do you determine if a function has an inverse?
4. What is the range of the function \( g(x) = x^2 + 4 \)?
5. How would the solution change if \( x \) could be negative?

#### Tip:
When finding the inverse of a quadratic function, remember to consider any domain restrictions to avoid non-real or negative values.

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 with x ≥ 0 and solve for g^{-1}(13). This problem covers key algebraic concepts, including inverse functions and quadratic equations. Suitable for high school students in Grades 9-11.

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