Decide whether the composite functions, f $$f \circ g$$ nd $\mathbf { g } \circ \mathrm { f }$ 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 $x$. 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 $x$.

Decide Whether the Composite Functions, F f∘gf \circ gf∘g Nd g∘f\mathbf { g } \circ \mathrm { f }g∘f

Decide Whether the Composite Functions, F $f \circ g$ Nd $\mathbf { g } \circ \mathrm { f }$