Question

type the correct answer in the box. use numerals instead of words. consider functions m and n: n(x) = (1/4)x² - 2x + 4 the value of m(n(2)) is. the value of n(m(1)) is.

Explanation:

Step1: Find n(2) using formula

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

Step2: Find m(1) from the graph

From the graph of $m(x)$, when $x=1$, $m(1)=2$

Step3: Calculate m(n(2))

Substitute $n(2)=1$ into $m(x)$: $m(n(2))=m(1)=2$

Step4: Find m(1) (already found in Step2)

$m(1)=2$

Step5: Calculate n(m(1))

Substitute $m(1)=2$ into $n(x)$: $n(m(1))=n(2)=1$

Answer:

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