Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Question
The image presents a mathematical exercise involving the composition of functions using a table. The task is to find the values of the compositions \((f \circ g)(10)\), \((g \circ f)(-10)\), \((f \circ f)(6)\), and \((g \circ g)(-6)\). ### Table Data: The table contains the following values: | \( x \) | \( -10 \) | \( -6 \) | \( -1 \) | \( 0 \) | \( 6 \) | \( 8 \) | \( 9 \) | \( 10 \) | |----------|---------|--------|-------|------|------|------|------|------| | \( f(x) \) | -10 | -10 | -6 | -1 | 6 | 8 | 8 | 0 | | \( g(x) \) | 6 | -10 | 8 | 0 | -6 | 10 | -1 | 9 | ### Calculations: 1. **\((f \circ g)(10)\):** - First, find \(g(10)\), which is 9. - Then, find \(f(9)\), which is 8. - Therefore, \((f \circ g)(10) = 8\). 2. **\((g \circ f)(-10)\):** - First, find \(f(-10)\), which is -10. - Then, find \(g(-10)\), which is 6. - Therefore, \((g \circ f)(-10) = 6\). 3. **\((f \circ f)(6)\):** - First, find \(f(6)\), which is 6. - Then, find \(f(6)\) again, which remains 6. - Therefore, \((f \circ f)(6) = 6\). 4. **\((g \circ g)(-6)\):** - First, find \(g(-6)\), which is -10. - Then, find \(g(-10)\), which is 6. - Therefore, \((g \circ g)(-6) = 6\
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Transcribed Image Text:The image presents a mathematical exercise involving the composition of functions using a table. The task is to find the values of the compositions \((f \circ g)(10)\), \((g \circ f)(-10)\), \((f \circ f)(6)\), and \((g \circ g)(-6)\). ### Table Data: The table contains the following values: | \( x \) | \( -10 \) | \( -6 \) | \( -1 \) | \( 0 \) | \( 6 \) | \( 8 \) | \( 9 \) | \( 10 \) | |----------|---------|--------|-------|------|------|------|------|------| | \( f(x) \) | -10 | -10 | -6 | -1 | 6 | 8 | 8 | 0 | | \( g(x) \) | 6 | -10 | 8 | 0 | -6 | 10 | -1 | 9 | ### Calculations: 1. **\((f \circ g)(10)\):** - First, find \(g(10)\), which is 9. - Then, find \(f(9)\), which is 8. - Therefore, \((f \circ g)(10) = 8\). 2. **\((g \circ f)(-10)\):** - First, find \(f(-10)\), which is -10. - Then, find \(g(-10)\), which is 6. - Therefore, \((g \circ f)(-10) = 6\). 3. **\((f \circ f)(6)\):** - First, find \(f(6)\), which is 6. - Then, find \(f(6)\) again, which remains 6. - Therefore, \((f \circ f)(6) = 6\). 4. **\((g \circ g)(-6)\):** - First, find \(g(-6)\), which is -10. - Then, find \(g(-10)\), which is 6. - Therefore, \((g \circ g)(-6) = 6\
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