Question

are the compositions of $f(x)=1$ and $g(x)=2$ commutative? why or why not? they are not commutative, because $f(g(x))$ and $g(f(x))$ are not equal. they are commutative, because $f(x)$ and $g(x)$ are constant functions. they are not commutative, because $f(x)$ and $g(x)$ are not equal. they are commutative, because $f(g(x))$ and $g(f(x))$ are constant functions.

Explanation:

Step1: Calculate $f(g(x))$

Since $g(x)=2$, substitute into $f$: $f(g(x))=f(2)=1$

Step2: Calculate $g(f(x))$

Since $f(x)=1$, substitute into $g$: $g(f(x))=g(1)=2$

Step3: Compare the two results

$f(g(x))=1$ and $g(f(x))=2$, so $f(g(x))
eq g(f(x))$

Step4: Evaluate the options

The correct reasoning is that the compositions are not equal.

Answer:

A. They are not commutative, because $f(g(x))$ and $g(f(x))$ are not equal.