Suppose that ƒ(x) = x2 and g(x) = | x | . Then thecompositions( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘ ƒ)(x) = | x2| = x2 are both differentiable at x = 0 even though g itself is not differentiable at x = 0. Does this contradict the Chain Rule? Explain.
Suppose that ƒ(x) = x2 and g(x) = | x | . Then thecompositions( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘ ƒ)(x) = | x2| = x2 are both differentiable at x = 0 even though g itself is not differentiable at x = 0. Does this contradict the Chain Rule? Explain.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.9: Combining Functions
Problem 50HP
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Suppose that ƒ(x) = x2 and g(x) = | x | . Then the
compositions
( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘ ƒ)(x) = | x2| = x2 are both
at x = 0. Does this contradict the Chain Rule? Explain.
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