Decide whether the composite functions, f ° g and g ° f, are equal to x.
-$$f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }$$
A) Yes, yes
B) No, yes
C) Yes, no
D) No, no

Question

Quizplus · Accepted Answer

For $f \circ g(x)$, we substitute $g(x) = x^2$ into $f$, getting $f(g(x)) = \sqrt{x^2 + 1}$, which is not equal to $x$ because of the "+1" inside the square root. For $g \circ f(x)$, we substitute $f(x) = \sqrt{x + 1}$ into $g$, getting $g(f(x)) = (\sqrt{x + 1})^2 = x + 1$, which is also not equal to $x$. Therefore, neither composite function equals $x$.

Decide Whether the Composite Functions, F ° G and G f(x)=x+1,g(x)=x2f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }f(x)=x+1​,g(x)=x2

Decide Whether the Composite Functions, F ° G and G $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }$