Question

O GRAPHS AND FUNCTIONSDomain of a rational function: Excluded values

Answer 1

Recall that the domain of a rational function consists of all the real numbers x except those for which the denominator is 0.

The denominator of the given rational function is:

`d(x)=x^2+11x-18.`

Notice that:

`\begin{gathered} x^2+11x+18=x^2+2x+9x+9*2 \\ =x(x+2)+9(x+2)=(x+9)(x+2). \end{gathered}`

Therefore d(x)=0 at x=-9 and x=-2, then those values are not in the domain of g.

Answer:

`x=-9,-2.`