Verified Answer :

Denominators of fractions cannot be zero, therefore the domain is all real numbers besides 2, for that is the only number that will falsify the fraction

Answer:

\(D=(-\infty,2)\cup (2,\infty), \{x|x eq2\}\)

Step-by-step explanation:

Given : Rational function \(f(x)=\frac{13}{2-x}\)

To find : State the domain of the rational function ?

Solution :

The domain of a rational function is defined as function consists of all the real numbers x except those for which the denominator is 0.

Rational function \(f(x)=\frac{13}{2-x}\)

Denominator = \(2-x\)

Put denominator = 0

\(2-x=0\)

\(x=2\)

Therefore, The domain of the rational function is all real numbers except 2.

or \(D=(-\infty,2)\cup (2,\infty), \{x|x eq2\}\)