the domain of the function.

f left parenthesis x right parenthesis equals StartFraction x plus 5 Over 2 minus x EndFractionf(x)=x+52−x




To find the domain of the function \( f(x) = \frac{x + 5}{2 - x} \), we need to determine for which values of \( x \) the function is defined.

Since division by zero is undefined, we must ensure that the denominator of the function is not zero. The denominator is \( 2 - x \), so we need to solve the equation:

\[
2 - x \neq 0
\]

Solving for \( x \):

\[
x \neq 2
\]

Thus, the function is undefined at \( x = 2 \). Therefore, the domain of \( f(x) \) is all real numbers except \( x = 2 \).

In interval notation, the domain is:

\[
(-\infty, 2) \cup (2, \infty)
\]

Would you like more details or have any further questions?

Here are 5 related questions to expand on this:
1. How does the domain of a rational function change if the numerator is also zero?
2. What happens to the graph of the function near \( x = 2 \)?
3. Can we simplify the function in any special cases?
4. What is the range of the function \( f(x) = \frac{x + 5}{2 - x} \)?
5. How would the domain change if there were a square root involved in the function?

**Tip**: Always check for values that make the denominator zero when finding the domain of rational functions.

The domain of the function f(x) = (x + 5) / (2 - x).

Explore how to find the domain of the rational function f(x) = (x + 5) / (2 - x). Understand why the function is undefined at x = 2 and learn how to express the domain in interval notation. Suitable for students in Grades 9-11.

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