We want to find the function which has a domain of x not equal to -2 and x not equal to 2
For this domain to exists, the function must not exist or be undefined at x = -2 and at x = 2
from the list of option given. Let us look for the option that is undefined at x = -2 and x = 2
Considering the third option
[tex]\begin{gathered} y=\frac{16}{4-x^2} \\ set\text{ the denominator to zero to find the points of discontinuity} \\ 4-x^2=0 \\ 4=x^2 \\ x^2=4 \\ x=\pm2 \\ \text{The function }y=\frac{16}{4-x^2}\text{ exists at all points except x=-2 and x=2} \end{gathered}[/tex]
Therefore, the correct option is
[tex]y=\frac{16}{4-x^2}[/tex]
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