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.