Question

given $g(x) = 2^{x + 1}$, evaluate the following.
(a) $g(3)$
(b) $g(1)$
(c) $g(-2)$
resources
read it watch it

Explanation:

Step1: Evaluate \( g(3) \)

Substitute \( x = 3 \) into \( g(x)=2^{x}+1 \). So \( g(3)=2^{3}+1 \). Calculate \( 2^{3}=8 \), then \( 8 + 1 = 9 \).

Step2: Evaluate \( g(1) \)

Substitute \( x = 1 \) into \( g(x)=2^{x}+1 \). So \( g(1)=2^{1}+1 \). Calculate \( 2^{1}=2 \), then \( 2 + 1 = 3 \).

Step3: Evaluate \( g(-2) \)

Substitute \( x = -2 \) into \( g(x)=2^{x}+1 \). So \( g(-2)=2^{-2}+1 \). Calculate \( 2^{-2}=\frac{1}{2^{2}}=\frac{1}{4} \), then \( \frac{1}{4}+1=\frac{1 + 4}{4}=\frac{5}{4}=1.25 \).

Answer:

(a) \( 9 \)
(b) \( 3 \)
(c) \( \frac{5}{4} \) (or \( 1.25 \))