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If f(x) = 4x²-3x+12 and g(x)=2x³+1, then the degree of the (fog)(x) is: a. 3 O b. 5 Oc. O d. 4 O e. 6 None

If f(x) = 4x²-3x+12 and g(x)=2x³+1, then the degree of the (fog)(x) is: a. 3 O b. 5 Oc. O d. 4 O e. 6 None

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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If \( f(x) = 4x^2 - 3x + 12 \) and \( g(x) = 2x^3 + 1 \), then the degree of the \( (f \circ g)(x) \) is: - a. 3 - b. 5 - c. None - d. 4 - e. 6 **Explanation:** To determine the degree of the composition \( (f \circ g)(x) \), which is \( f(g(x)) \): 1. Note the degree of \( g(x) \), which is 3, as the highest power of \( x \) in \( g(x) \) is \( x^3 \). 2. Substitute \( g(x) \) into \( f(x) \). \( f(g(x)) = 4(g(x))^2 - 3(g(x)) + 12 \). 3. The degree of \( f(g(x)) \) will be twice the degree of \( g(x) \), because \( f(x) \) is a polynomial of degree 2. 4. Therefore, the degree is \( 2 \times 3 = 6 \). So, the correct answer is e. 6.
Transcribed Image Text:If \( f(x) = 4x^2 - 3x + 12 \) and \( g(x) = 2x^3 + 1 \), then the degree of the \( (f \circ g)(x) \) is: - a. 3 - b. 5 - c. None - d. 4 - e. 6 **Explanation:** To determine the degree of the composition \( (f \circ g)(x) \), which is \( f(g(x)) \): 1. Note the degree of \( g(x) \), which is 3, as the highest power of \( x \) in \( g(x) \) is \( x^3 \). 2. Substitute \( g(x) \) into \( f(x) \). \( f(g(x)) = 4(g(x))^2 - 3(g(x)) + 12 \). 3. The degree of \( f(g(x)) \) will be twice the degree of \( g(x) \), because \( f(x) \) is a polynomial of degree 2. 4. Therefore, the degree is \( 2 \times 3 = 6 \). So, the correct answer is e. 6.
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