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The problem asks to determine the image of \( x = 1 \) under the function \( g(x) = \frac{x^2 - 2}{x^2 + x} \).

We need to find \( g(1) \) by substituting \( x = 1 \) into the given function. Let me calculate this.

The function is:

\[
g(x) = \frac{x^2 - 2}{x^2 + x}
\]

Substituting \( x = 1 \):

\[
g(1) = \frac{1^2 - 2}{1^2 + 1} = \frac{1 - 2}{1 + 1} = \frac{-1}{2} = -0.5
\]

So, the image of \( 1 \) under the function \( g(x) \) is \( -0.500 \) (rounded to three decimal places).

Would you like further details or have any questions about this solution?

Here are 5 related questions to deepen your understanding:

1. How would you compute \( g(2) \) using the same function?
2. What is the domain of the function \( g(x) \)?
3. How do you find the vertical and horizontal asymptotes of \( g(x) \)?
4. Can you rewrite \( g(x) \) in partial fraction form if possible?
5. How would you determine the critical points of the function \( g(x) \)?

**Tip:** When calculating the image of a function at a certain point, always check the domain to ensure the point is included.

Determina la imagen de 1 bajo la función g(x) = (x^2 - 2) / (x^2 + x).

Find the image of x = 1 under the function g(x) = (x^2 - 2) / (x^2 + x). This solution involves substitution and basic algebraic manipulation, making it suitable for students in Grades 10-12.

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