We are given that $g(x) = x^2$. Let's solve each part:

a) $g(1)$

$g(1) = 1^2 = 1$

b) $g(-2)$

$g(-2) = (-2)^2 = 4$

c) $g(-x)$

$g(-x) = (-x)^2 = x^2$

d) $g(2y)$

$g(2y) = (2y)^2 = 4y^2$

e) $g(1+h)$

$g(1+h) = (1+h)^2 = 1^2 + 2(1)(h) + h^2 = 1 + 2h + h^2$

If you have any questions or need further details, feel free to ask! Here are 5 related questions to expand your understanding:

1. What is the derivative of $g(x) = x^2$?
2. How does $g(-x)$ compare to $g(x)$ in general?
3. Can you find $g(a+b)$ for arbitrary constants $a$ and $b$?
4. What happens to the function $g(x) = x^2$ as $x \to \infty$?
5. Can you find $g(x^2)$ for any given $x$?

Tip: Always remember that squaring a negative value results in a positive number, as in part c where $g(-x) = g(x)$.