To find the value of [tex]\( g(-3) \)[/tex] for the function [tex]\( g(x) = 14 f(x) \)[/tex]:
1. Identify [tex]\( f(-3) \)[/tex] from the table:
- The table provides values of [tex]\( f(x) \)[/tex] corresponding to different [tex]\( x \)[/tex] values.
- From the table, when [tex]\( x = -3 \)[/tex], the value of [tex]\( f(-3) = 2 \)[/tex].
2. Determine the value of [tex]\( g(-3) \)[/tex]:
- Given that [tex]\( g(x) = 14 f(x) \)[/tex], you need to substitute [tex]\( x = -3 \)[/tex] into the equation for [tex]\( g \)[/tex].
- So, [tex]\( g(-3) = 14 f(-3) \)[/tex].
3. Calculate [tex]\( g(-3) \)[/tex]:
- Substitute the previously found [tex]\( f(-3) = 2 \)[/tex] into the equation for [tex]\( g \)[/tex].
- Therefore, [tex]\( g(-3) = 14 \times 2 = 28 \)[/tex].
So, the value of [tex]\( g(-3) \)[/tex] is [tex]\(\boxed{28}\)[/tex].
