Question

Find all the values of x that are not in the domain of h

Answer 1

By definition, the domain of a function is the set of all the input values for which the function is defined.

Given the function:

`h\mleft(x\mright)=(x^2-5x-14)/(x^2-49)`

You can identify that it is a Rational Function because it has this form:

`f(x)=(p(x))/(q(x))`

Where these are polynomials:

`\begin{gathered} p(x) \\ q(x) \end{gathered}`

For Rational Functions:

`q(x)\\e0`

Then, since the denominator cannot be zero, you need to find the values of "x" that make it equal to zero. To do this, you have to set up that:

`x^2-49=0`

Now you have to solve for "x":

`\begin{gathered} x^2=49 \\ x=\pm\sqrt[]{49} \\ \\ x_1=7 \\ x_2=-7 \end{gathered}`

Therefore, the answer is:

`x=7,-7`