Determine whether the statement is true or false.
If f(x)= x + 1 and g(x)= 5x,then $( f \circ g ) ( x ) = ( g \circ f ) ( x )$ .

A)False
B)True

Question

Determine whether the statement is true or false. ​
If f(x)= x + 1 and g(x)= 5x,then $( f \circ g ) ( x ) = ( g \circ f ) ( x )$ .
​
A)False
B)True

Quizplus · Accepted Answer

The composition $(f \circ g)(x)$ means applying $g$ first and then $f$, resulting in $f(g(x)) = f(5x) = 5x + 1$. Conversely, $(g \circ f)(x)$ means applying $f$ first and then $g$, resulting in $g(f(x)) = g(x + 1) = 5(x + 1) = 5x + 5$. Since $5x + 1 \neq 5x + 5$, the statement is false.

Determine Whether the Statement Is True or False (f∘g)(x)=(g∘f)(x)( f \circ g ) ( x ) = ( g \circ f ) ( x )(f∘g)(x)=(g∘f)(x)

Determine Whether the Statement Is True or False $( f \circ g ) ( x ) = ( g \circ f ) ( x )$