To determine the domain of the function \( f(x) = \frac{11x + 22}{5x - 5} \), we need to find the values of \( x \) that make the function undefined.

A function is undefined where the denominator equals zero, so we set the denominator equal to zero and solve for \( x \):

\[
5x - 5 = 0
\]
\[
5x = 5
\]
\[
x = 1
\]

Thus, the function is undefined at \( x = 1 \). Therefore, the domain of \( f(x) \) is all real numbers except \( x = 1 \).

In interval notation, the domain is:
\[
(-\infty, 1) \cup (1, +\infty)
\]

Would you like more details or have any questions? Here are some related problems:

1. What is the range of \( f(x) = \frac{11x + 22}{5x - 5} \)?
2. Find the vertical asymptote of \( f(x) = \frac{11x + 22}{5x - 5} \).
3. Simplify the expression \( \frac{11x + 22}{5x - 5} \) if possible.
4. Determine the horizontal asymptote of \( f(x) = \frac{11x + 22}{5x - 5} \).
5. What is the behavior of the function as \( x \) approaches \( 1 \)?

**Tip:** Always check where the denominator of a rational function equals zero to find its domain!

Discover how to determine the domain of the rational function f(x) = (11x + 22) / (5x - 5). This solution explains how to find values that make the function undefined by solving the denominator. Suitable for high school students in Grades 9-11.

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