Question

a) for what values of x is the function f(x) = \frac{20}{x + 6} undefined? separate multiple values with a comma and if there are no such values, enter none.

Explanation:

Step1: Recall when a rational function is undefined

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

Step2: Set the denominator equal to zero and solve for \( x \)

For the function \( f(x)=\frac{20}{x + 6} \), the denominator is \( x+6 \). We set \( x + 6=0 \).
Solving the equation \( x+6 = 0 \), we subtract 6 from both sides: \( x= - 6 \).

Answer:

\( -6 \)