Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To solve for [tex]\((g \circ f)(3)\)[/tex], we need to follow these steps:
1. Find [tex]\( f(3) \)[/tex]:
- We are given the function [tex]\( f(x) = 4x + 2 \)[/tex].
- Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(3) = 4(3) + 2 = 12 + 2 = 14 \][/tex]
2. Now, use the result of [tex]\( f(3) \)[/tex] to find [tex]\( g(f(3)) \)[/tex]:
- We found [tex]\( f(3) = 14 \)[/tex].
- Next, we are given the function [tex]\( g(x) = x^2 - 2x - 5 \)[/tex].
- Substitute [tex]\( x = 14 \)[/tex] into the function [tex]\( g(x) \)[/tex]:
[tex]\[ g(14) = 14^2 - 2(14) - 5 \][/tex]
3. Calculate [tex]\( g(14) \)[/tex]:
- First, compute [tex]\( 14^2 \)[/tex]:
[tex]\[ 14^2 = 196 \][/tex]
- Then, compute [tex]\( 2(14) \)[/tex]:
[tex]\[ 2(14) = 28 \][/tex]
- Now, substitute these values back into [tex]\( g(14) \)[/tex]:
[tex]\[ g(14) = 196 - 28 - 5 = 168 - 5 = 163 \][/tex]
Therefore, the value of [tex]\((g \circ f)(3)\)[/tex] is [tex]\(163\)[/tex].
1. Find [tex]\( f(3) \)[/tex]:
- We are given the function [tex]\( f(x) = 4x + 2 \)[/tex].
- Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(3) = 4(3) + 2 = 12 + 2 = 14 \][/tex]
2. Now, use the result of [tex]\( f(3) \)[/tex] to find [tex]\( g(f(3)) \)[/tex]:
- We found [tex]\( f(3) = 14 \)[/tex].
- Next, we are given the function [tex]\( g(x) = x^2 - 2x - 5 \)[/tex].
- Substitute [tex]\( x = 14 \)[/tex] into the function [tex]\( g(x) \)[/tex]:
[tex]\[ g(14) = 14^2 - 2(14) - 5 \][/tex]
3. Calculate [tex]\( g(14) \)[/tex]:
- First, compute [tex]\( 14^2 \)[/tex]:
[tex]\[ 14^2 = 196 \][/tex]
- Then, compute [tex]\( 2(14) \)[/tex]:
[tex]\[ 2(14) = 28 \][/tex]
- Now, substitute these values back into [tex]\( g(14) \)[/tex]:
[tex]\[ g(14) = 196 - 28 - 5 = 168 - 5 = 163 \][/tex]
Therefore, the value of [tex]\((g \circ f)(3)\)[/tex] is [tex]\(163\)[/tex].
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.