Question

complete the following statements using $m(x)=x^2$ and $n(x)=x - 3$.
$m(n(x))=m(x - 3)$
$=\boldsymbol{\downarrow}^2$
$n(m(x))=n(x^2)$
$=x^2\boldsymbol{\downarrow}$
because $m(n(x))\boldsymbol{\downarrow}n(m(x))$, the composition of $m$ and $n$ is not commutative.
therefore, function composition is not commutative.

Explanation:

Step1: Substitute into $m(x)$

Since $m(x)=x^2$, replace $x$ with $x-3$:
$m(x-3)=(x-3)^2$, so the blank is $x-3$.

Step2: Substitute into $n(x)$

Since $n(x)=x-3$, replace $x$ with $x^2$:
$n(x^2)=x^2-3$, so the blank is $3$.

Step3: Compare the two composites

Expand $m(n(x))=(x-3)^2=x^2-6x+9$, and $n(m(x))=x^2-3$. These are not equal, so the blank is $
eq$.

Answer:

1. $x-3$
2. $3$
3. $

eq$