Explore a diverse range of topics and get answers from knowledgeable individuals on IDNLearn.com. Ask anything and receive immediate, well-informed answers from our dedicated community of experts.
Sagot :
Let's solve the given problem step-by-step.
We have two functions defined as:
1. [tex]\( f(x) = 5x + 7 \)[/tex]
2. [tex]\( g(x) = -2x - 4 \)[/tex]
We need to find the composition [tex]\( g(f(x)) \)[/tex]. Let's break this down.
Step 1: Compute [tex]\( f(x) \)[/tex].
Given [tex]\( f(x) = 5x + 7 \)[/tex].
Step 2: Substitute [tex]\( f(x) \)[/tex] into [tex]\( g(x) \)[/tex].
We need to find [tex]\( g(f(x)) \)[/tex]. From the definition of [tex]\( g(x) \)[/tex]:
[tex]\[ g(x) = -2x - 4 \][/tex]
Replace [tex]\( x \)[/tex] in [tex]\( g(x) \)[/tex] with [tex]\( f(x) \)[/tex]:
[tex]\[ g(f(x)) = g(5x + 7) \][/tex]
Step 3: Evaluate [tex]\( g(f(x)) \)[/tex].
Substitute [tex]\( 5x + 7 \)[/tex] for [tex]\( x \)[/tex] in [tex]\( g(x) \)[/tex]:
[tex]\[ g(5x + 7) = -2(5x + 7) - 4 \][/tex]
Step 4: Simplify the expression.
First, distribute [tex]\(-2\)[/tex] through the parentheses:
[tex]\[ -2(5x + 7) = -10x - 14 \][/tex]
Then, subtract 4:
[tex]\[ -10x - 14 - 4 = -10x - 18 \][/tex]
So, the final form of the composite function [tex]\( g(f(x)) \)[/tex] is:
[tex]\[ g(f(x)) = -10x - 18 \][/tex]
Thus, the coefficient of [tex]\( x \)[/tex] in the expression [tex]\( g(f(x)) \)[/tex] is [tex]\(-10\)[/tex], and the constant term is [tex]\(-18\)[/tex]. Therefore, the missing term in [tex]\( g(f(x)) = -10x + [?] \)[/tex] is:
[tex]\[ \boxed{-18} \][/tex]
We have two functions defined as:
1. [tex]\( f(x) = 5x + 7 \)[/tex]
2. [tex]\( g(x) = -2x - 4 \)[/tex]
We need to find the composition [tex]\( g(f(x)) \)[/tex]. Let's break this down.
Step 1: Compute [tex]\( f(x) \)[/tex].
Given [tex]\( f(x) = 5x + 7 \)[/tex].
Step 2: Substitute [tex]\( f(x) \)[/tex] into [tex]\( g(x) \)[/tex].
We need to find [tex]\( g(f(x)) \)[/tex]. From the definition of [tex]\( g(x) \)[/tex]:
[tex]\[ g(x) = -2x - 4 \][/tex]
Replace [tex]\( x \)[/tex] in [tex]\( g(x) \)[/tex] with [tex]\( f(x) \)[/tex]:
[tex]\[ g(f(x)) = g(5x + 7) \][/tex]
Step 3: Evaluate [tex]\( g(f(x)) \)[/tex].
Substitute [tex]\( 5x + 7 \)[/tex] for [tex]\( x \)[/tex] in [tex]\( g(x) \)[/tex]:
[tex]\[ g(5x + 7) = -2(5x + 7) - 4 \][/tex]
Step 4: Simplify the expression.
First, distribute [tex]\(-2\)[/tex] through the parentheses:
[tex]\[ -2(5x + 7) = -10x - 14 \][/tex]
Then, subtract 4:
[tex]\[ -10x - 14 - 4 = -10x - 18 \][/tex]
So, the final form of the composite function [tex]\( g(f(x)) \)[/tex] is:
[tex]\[ g(f(x)) = -10x - 18 \][/tex]
Thus, the coefficient of [tex]\( x \)[/tex] in the expression [tex]\( g(f(x)) \)[/tex] is [tex]\(-10\)[/tex], and the constant term is [tex]\(-18\)[/tex]. Therefore, the missing term in [tex]\( g(f(x)) = -10x + [?] \)[/tex] is:
[tex]\[ \boxed{-18} \][/tex]
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.