Decide whether the composite functions, f $$f \circ g$$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x.
-$f ( x ) = 2 x , \quad g ( x ) = \frac { x } { 2 }$
A) No, no
B) No, yes
C) Yes, no
D) Yes, yes

Question

Quizplus · Accepted Answer

For $f \circ g$, we substitute $g(x) = \frac{x}{2}$ into $f$, getting $f(g(x)) = 2\left(\frac{x}{2}\right) = x$. For $g \circ f$, we substitute $f(x) = 2x$ into $g$, getting $g(f(x)) = \frac{2x}{2} = x$. Thus, both composite functions are 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 $\mathbf { g } \circ \mathrm { f }$