Question

m(x) = x² + 4x
n(x) = x
(mn)(x) =
x² + 4x(x)
(x² + 4x)(x) ✔️
complete
which is equal to:
x³ + 4x² ✔️
5x²
4x⁴
complete
evaluate (mn)(x) for x = -3.
(mn)(-3) = 9 ✔️
complete
\\(\frac{m}{n}(x)\\), \\(x \
eq \square\\)
done ✔️

Explanation:

To determine the value of \( x \) for which \( \frac{m}{n}(x) \) is undefined, we analyze the denominator of the rational function.

Step 1: Recall the condition for undefined rational functions

A rational function \( \frac{f(x)}{g(x)} \) is undefined when the denominator \( g(x) = 0 \), because division by zero is undefined in mathematics.

Step 2: Identify the denominator function

For \( \frac{m}{n}(x) \), the denominator function is \( n(x) \). From the given information, \( n(x) = x \).

Step 3: Solve for \( x \) when the denominator is zero

We set the denominator equal to zero and solve for \( x \):
\[
n(x) = 0 \implies x = 0
\]

Thus, \( \frac{m}{n}(x) \) is undefined when \( x = 0 \), so \( x
eq 0 \).

Answer:

\( \boxed{0} \)