Sure, let's find the value of the function [tex]\( g(x) = 3x^2 + 5 \)[/tex] at [tex]\( x = -3 \)[/tex].
1. Function Definition: We start with the function [tex]\( g(x) = 3x^2 + 5 \)[/tex].
2. Substitute [tex]\( x = -3 \)[/tex]: To find [tex]\( g(-3) \)[/tex], substitute [tex]\( -3 \)[/tex] into the function [tex]\( g(x) \)[/tex].
[tex]\[
g(-3) = 3(-3)^2 + 5
\][/tex]
3. Calculate the Square: Compute the square of [tex]\( -3 \)[/tex].
[tex]\[
(-3)^2 = 9
\][/tex]
4. Multiply by 3: Multiply 9 by 3.
[tex]\[
3 \times 9 = 27
\][/tex]
5. Add 5: Add 5 to the result from the previous step.
[tex]\[
27 + 5 = 32
\][/tex]
Therefore, the value of [tex]\( g(-3) \)[/tex] is [tex]\( 32 \)[/tex].
