Math Problem Statement
Quiz:Chapter 4 Skills Check Quiz (Integrated Review) Question 1 of 4 This quiz: 4 point(s) possible This question: 1 point(s) possible
Skip to Main content Question 1 Question 2 Question 3 Question 4 Question content area top Part 1 Let f(x)equalsStartAbsoluteValue x EndAbsoluteValue, g(x)equalsxminus2, and h(x)equalsx squared. Write N(x)equalsxminus4 as a composition of functions. Question content area bottom Part 1 Choose the following composition that correctly defines N(x)equalsxminus4. A. gcircleg B. fcirclegcircleh C. gcircleh D. hcircleg Choose the following composition that correctly defines N(x)x4.
Solution
To write as a composition of functions, let's analyze the options.
Given Functions:
We need to form using these functions.
Composition Analysis:
Option A:
- , so .
- This matches .
Option B:
- This involves applying , , and , which does not result in .
- This does not match .
Option C:
- , which is not .
- This does not match .
Option D:
- , which is not .
- This does not match .
Correct Answer:
A.
Would you like me to explain further or assist with additional concepts?
Relative Questions:
- How do you compose functions step by step?
- What are the common properties of function compositions?
- Can compositions include transformations like reflection or scaling?
- What happens when absolute value functions are composed with other types of functions?
- How do quadratic functions behave when part of a composition?
Tip: Always check the intermediate steps in a composition to ensure the final function matches the target expression.
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Math Problem Analysis
Mathematical Concepts
Function Composition
Linear Functions
Formulas
Composition of Functions: (f ∘ g)(x) = f(g(x))
Theorems
Properties of Function Composition
Suitable Grade Level
Grades 9-11
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