To determine the zeros of the function [tex]\( g \)[/tex], we need to identify the values of [tex]\( x \)[/tex] that make the function equal to zero. The given factors of the function are [tex]\((x-7)\)[/tex] and [tex]\((x+6)\)[/tex].
1. First, set each factor equal to zero and solve for [tex]\( x \)[/tex].
For the factor [tex]\((x-7)\)[/tex]:
[tex]\[ x - 7 = 0 \][/tex]
Add 7 to both sides:
[tex]\[ x = 7 \][/tex]
For the factor [tex]\((x+6)\)[/tex]:
[tex]\[ x + 6 = 0 \][/tex]
Subtract 6 from both sides:
[tex]\[ x = -6 \][/tex]
Thus, the zeros of the function [tex]\( g \)[/tex] are [tex]\( x = 7 \)[/tex] and [tex]\( x = -6 \)[/tex].
So, the correct answer is:
B. [tex]\(-6\)[/tex] and 7
