By definition, the domain of a function is the set of all the input values for which the function is defined.
Given the function:
[tex]h\mleft(x\mright)=\frac{x^2-5x-14}{x^2-49}[/tex]
You can identify that it is a Rational Function because it has this form:
[tex]f(x)=\frac{p(x)}{q(x)}[/tex]
Where these are polynomials:
[tex]\begin{gathered} p(x) \\ q(x) \end{gathered}[/tex]
For Rational Functions:
[tex]q(x)\ne0[/tex]
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:
[tex]x^2-49=0[/tex]
Now you have to solve for "x":
[tex]\begin{gathered} x^2=49 \\ x=\pm\sqrt[]{49} \\ \\ x_1=7 \\ x_2=-7 \end{gathered}[/tex]
Therefore, the answer is:
[tex]x=7,-7[/tex]
