To solve for [tex]\( g(-1) \)[/tex] where the function [tex]\( g(x) = 5x^2 + 2x \)[/tex]:
1. Substitute [tex]\(-1\)[/tex] into the function [tex]\( g(x) \)[/tex]:
We need to find [tex]\( g(-1) \)[/tex].
So, we will substitute [tex]\( x = -1 \)[/tex] into the equation [tex]\( g(x) \)[/tex]:
[tex]\[
g(-1) = 5(-1)^2 + 2(-1)
\][/tex]
2. Calculate the squared term:
Evaluate [tex]\((-1)^2\)[/tex]:
[tex]\[
(-1)^2 = 1
\][/tex]
So the equation becomes:
[tex]\[
g(-1) = 5 \cdot 1 + 2(-1)
\][/tex]
3. Multiply by 5:
[tex]\[
5 \cdot 1 = 5
\][/tex]
Now the equation is:
[tex]\[
g(-1) = 5 + 2(-1)
\][/tex]
4. Multiply by 2:
[tex]\[
2 \cdot (-1) = -2
\][/tex]
Now the equation is:
[tex]\[
g(-1) = 5 - 2
\][/tex]
5. Perform the addition/subtraction:
[tex]\[
g(-1) = 5 - 2 = 3
\][/tex]
Therefore, the value of [tex]\( g(-1) \)[/tex] is [tex]\( \boxed{3} \)[/tex].
