Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.7 - Combining Functions - 2.7 Exercises - Page 217: 56

Answer

f∘g $ \frac {1}{\sqrt{x^2 - 4x}}$ Domain: (-∞, 0) U (4, ∞) g∘f $\frac{1}{x} - \frac{4}{\sqrt x}$ Domain: (0, ∞) f∘f $\sqrt x$ Domain: (0, ∞) g∘g $x^4 - 8x^3 + 12x^2 + 16x$ Domain: (- ∞, ∞)

Work Step by Step

$f(x) = \frac{1}{\sqrt x}$ $g(x) = x^2 - 4x $ f∘g $f(x^2 - 4x) = \frac {1}{\sqrt{x^2 - 4x}}$ Domain: (-∞, 0) U (4, ∞) g∘f $g(\frac{1}{\sqrt x}) = (\frac{1}{\sqrt x})^{2} - 4(\frac{1}{\sqrt x})$ =$\frac{1}{x} - \frac{4}{\sqrt x}$ Domain: (0, ∞) f∘f $f(\frac{1}{\sqrt x}) = \frac{1}{\frac{1}{\sqrt x}}$ =$\sqrt x$ Domain: (0, ∞) g∘g $g(x^2 - 4x) = (x^2 - 4x)^2 - 4(x^2 - 4x) $ =$x^4 - 8x^3 + 12x^2 + 16x$ Domain: (- ∞, ∞)
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