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Use the functions to determine the value of each composite function algebraically. f(x) = 2x² g(x) = 3x - 2 h(x) = 3-4x (fog)(3) = (hj)(12) = (goh)(x) = 6 j(x) == (hog)(x) =

Use the functions to determine the value of each composite function algebraically. f(x) = 2x² g(x) = 3x - 2 h(x) = 3-4x (fog)(3) = (hj)(12) = (goh)(x) = 6 j(x) == (hog)(x) =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Composite Functions Evaluation Use the functions to determine the value of each composite function algebraically. #### Given Functions: - \( f(x) = 2x^2 \) - \( g(x) = 3x - 2 \) - \( h(x) = 3 - 4x \) - \( j(x) = \frac{6}{x} \) #### Composite Functions: 1. **Evaluate \( (f \circ g)(3) \):** - Find the value of the composite function \( f(g(3)) \). 2. **Evaluate \( (h \circ j)(12) \):** - Find the value of the composite function \( h(j(12)) \). 3. **Evaluate \( (g \circ h)(x) \):** - Determine the expression for the composite function \( g(h(x)) \). 4. **Evaluate \( (h \circ g)(x) \):** - Determine the expression for the composite function \( h(g(x)) \).
Transcribed Image Text:### Composite Functions Evaluation Use the functions to determine the value of each composite function algebraically. #### Given Functions: - \( f(x) = 2x^2 \) - \( g(x) = 3x - 2 \) - \( h(x) = 3 - 4x \) - \( j(x) = \frac{6}{x} \) #### Composite Functions: 1. **Evaluate \( (f \circ g)(3) \):** - Find the value of the composite function \( f(g(3)) \). 2. **Evaluate \( (h \circ j)(12) \):** - Find the value of the composite function \( h(j(12)) \). 3. **Evaluate \( (g \circ h)(x) \):** - Determine the expression for the composite function \( g(h(x)) \). 4. **Evaluate \( (h \circ g)(x) \):** - Determine the expression for the composite function \( h(g(x)) \).
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