Question

Find the domain. Then use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters. f(x)= \frac{x-3}{x^2+9x-22} AnswerAnswer,AnswerAnswerUAnswerAnswer,AnswerAnswerUAnswerAnswer,AnswerAnswer

Answer 1

The domain of a function is all the x values that x can take.

We have the next function:

$f(x)=\frac{x-3}{x^2+9x-22}$

Now, we need to find when the denominator is undefined.

The denominator can be 0.

So equal the whole expression to 0.

Therefore:

$x^2+9x-22=0$

To find the x value, use the quadratic formula, which is given by:

$x=\frac{-b\pm\sqrt[2]{b^2-4ac}}{2a}$

Replace this values using a=1, b=9 and c= -22

$x=\frac{-9\pm\sqrt[]{9^2-4(1)(-22)}}{2(1)}$$x=\frac{9\pm13}{2}$

Then x will take two values:

$x_1=\frac{-9-13}{2}=\frac{-22}{2}=-11_{}$$x_2=\frac{-9+13}{2}=\frac{4}{2}=-2_{}$

So, when x= -11 and x=2, the function is undefined.

Finally, we can find the domain: (-inf, -11) U (-11,2) U (2, inf)