Question

type the correct answer in the box. use numerals instead of words. consider functions m and n: n(x) = \frac{1}{4}x^2 - 2x + 4 the value of m(n(2)) is \boxed{1} the value of n(m(1)) is \boxed{}

Explanation:

Step1: Calculate n(2) first

Substitute $x=2$ into $n(x)$:
$$n(2)=\frac{1}{4}(2)^2 - 2(2) + 4$$
$$=\frac{1}{4}(4) - 4 + 4$$
$$=1 - 4 + 4 = 1$$

Step2: Find m(n(2))=m(1)

From the graph, when $x=1$, $m(1)=1$

Step3: Calculate m(1) from graph

As above, $m(1)=1$

Step4: Calculate n(m(1))=n(1)

Substitute $x=1$ into $n(x)$:
$$n(1)=\frac{1}{4}(1)^2 - 2(1) + 4$$
$$=\frac{1}{4} - 2 + 4$$
$$=\frac{1}{4} + 2 = \frac{9}{4} = 2.25$$

Answer:

The value of $m(n(2))$ is 1
The value of $n(m(1))$ is 2.25