For each pair of functions, find f(g(x)) and g(f(x)). Simplify your answers. 1 7 1 2 21. f(x)== -₁ 8(x) = ² + + 6 22. f(x)=¹4, 8(x)=²+4 X-6 X X-4 23. f(x)=x² +1, g(x)=√√x+2 24. f(x)=√√x+2, g(x)=x² +3
For each pair of functions, find f(g(x)) and g(f(x)). Simplify your answers. 1 7 1 2 21. f(x)== -₁ 8(x) = ² + + 6 22. f(x)=¹4, 8(x)=²+4 X-6 X X-4 23. f(x)=x² +1, g(x)=√√x+2 24. f(x)=√√x+2, g(x)=x² +3
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![For each pair of functions, find \( f(g(x)) \) and \( g(f(x)) \). Simplify your answers.
\[ 21. \ f(x) = \frac{1}{x-6}, \ g(x) = \frac{7}{x} + 6 \]
\[ 22. \ f(x) = \frac{1}{x-4}, \ g(x) = \frac{2}{x} + 4 \]
\[ 23. \ f(x) = x^2 + 1, \ g(x) = \sqrt{x+2} \]
\[ 24. \ f(x) = \sqrt{x+2}, \ g(x) = x^2 + 3 \]
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Find the domain of
\[ 1. \ (f \circ g)(x) \text{ where } f(x) = \frac{5}{x-1} \text{ and } g(x) = \frac{4}{3x-2} \]
\[ 2. \ (f \circ g)(x) \text{ where } f(x) = \sqrt{x+2} \text{ and } g(x) = \sqrt{3-x} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F033f8f0e-92d7-4ac0-8a46-2219233ed0fb%2Fa041a333-6791-43ed-83ee-7a0bcb8633f4%2Fvguhotu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For each pair of functions, find \( f(g(x)) \) and \( g(f(x)) \). Simplify your answers.
\[ 21. \ f(x) = \frac{1}{x-6}, \ g(x) = \frac{7}{x} + 6 \]
\[ 22. \ f(x) = \frac{1}{x-4}, \ g(x) = \frac{2}{x} + 4 \]
\[ 23. \ f(x) = x^2 + 1, \ g(x) = \sqrt{x+2} \]
\[ 24. \ f(x) = \sqrt{x+2}, \ g(x) = x^2 + 3 \]
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Find the domain of
\[ 1. \ (f \circ g)(x) \text{ where } f(x) = \frac{5}{x-1} \text{ and } g(x) = \frac{4}{3x-2} \]
\[ 2. \ (f \circ g)(x) \text{ where } f(x) = \sqrt{x+2} \text{ and } g(x) = \sqrt{3-x} \]
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