Decide whether the composite functions, f ° g and g ° f, are equal to x.
-$$f ( x ) = \sqrt { x } , g ( x ) = x ^ { 2 }$$
A) No, no
B) Yes, yes
C) Yes, no
D) No, yes

Name: Decide whether the composite functions, f ° g and g ° f, are equal to x. -\[f ( x ) = \sqrt { x } , g ( x ) = x ^ { 2 }\] A) No, no B) Yes, yes C) Yes, no D) No, yes
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Question

Quizplus · Accepted Answer

f ° g(x) = f(g(x)) = f(x^2) = √(x^2) = |x|g ° f(x) = g(f(x)) = g(√x) = (√x)^2 = xSo, f ° g(x) ≠ g ° f(x) ≠ x

Decide Whether the Composite Functions, F ° G and G f(x)=x,g(x)=x2f ( x ) = \sqrt { x } , g ( x ) = x ^ { 2 }f(x)=x​,g(x)=x2

Decide Whether the Composite Functions, F ° G and G $f ( x ) = \sqrt { x } , g ( x ) = x ^ { 2 }$