Given the function $g(x) = 2^x + 1$, we can evaluate it at the specified values:

(a) $g(3)$

$g(3) = 2^3 + 1 = 8 + 1 = 9$

(b) $g(2)$

$g(2) = 2^2 + 1 = 4 + 1 = 5$

(c) $g(-2)$

$g(-2) = 2^{-2} + 1 = \frac{1}{2^2} + 1 = \frac{1}{4} + 1 = 1.25$

Thus, the results are:

• $g(3) = 9$
• $g(2) = 5$
• $g(-2) = 1.25$

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. What is the general behavior of $g(x)$ as $x$ increases or decreases?
2. How would you calculate $g(x)$ for fractional values of $x$?
3. What is the inverse of $g(x)$, if it exists?
4. How does $g(x)$ compare to other exponential functions, like $g(x) = 3^x + 1$?
5. Can you graph $g(x) = 2^x + 1$ and describe its shape?

Tip: For negative exponents, $2^{-x} = \frac{1}{2^x}$, which makes the function decrease as $x$ becomes more negative.