Answer :
Certainly! Let's solve the problem step-by-step to find [tex]\( f(g(-3)) \)[/tex] given the functions [tex]\( f(x) = 2x + 1 \)[/tex] and [tex]\( g(x) = 4x \)[/tex].
1. Calculate [tex]\( g(-3) \)[/tex]:
- The function [tex]\( g(x) \)[/tex] is given as [tex]\( g(x) = 4x \)[/tex].
- Substitute [tex]\( x = -3 \)[/tex] into the function [tex]\( g \)[/tex]:
[tex]\[ g(-3) = 4(-3) = -12 \][/tex]
2. Calculate [tex]\( f(g(-3)) \)[/tex]:
- We have already found that [tex]\( g(-3) = -12 \)[/tex].
- Next, we need to find [tex]\( f(g(-3)) \)[/tex], which is [tex]\( f(-12) \)[/tex].
- The function [tex]\( f(x) \)[/tex] is given as [tex]\( f(x) = 2x + 1 \)[/tex].
- Substitute [tex]\( x = -12 \)[/tex] into the function [tex]\( f \)[/tex]:
[tex]\[ f(-12) = 2(-12) + 1 = -24 + 1 = -23 \][/tex]
Therefore, [tex]\( f(g(-3)) = -23 \)[/tex].
So, the correct answer is [tex]\(\boxed{-23}\)[/tex].
1. Calculate [tex]\( g(-3) \)[/tex]:
- The function [tex]\( g(x) \)[/tex] is given as [tex]\( g(x) = 4x \)[/tex].
- Substitute [tex]\( x = -3 \)[/tex] into the function [tex]\( g \)[/tex]:
[tex]\[ g(-3) = 4(-3) = -12 \][/tex]
2. Calculate [tex]\( f(g(-3)) \)[/tex]:
- We have already found that [tex]\( g(-3) = -12 \)[/tex].
- Next, we need to find [tex]\( f(g(-3)) \)[/tex], which is [tex]\( f(-12) \)[/tex].
- The function [tex]\( f(x) \)[/tex] is given as [tex]\( f(x) = 2x + 1 \)[/tex].
- Substitute [tex]\( x = -12 \)[/tex] into the function [tex]\( f \)[/tex]:
[tex]\[ f(-12) = 2(-12) + 1 = -24 + 1 = -23 \][/tex]
Therefore, [tex]\( f(g(-3)) = -23 \)[/tex].
So, the correct answer is [tex]\(\boxed{-23}\)[/tex].
