The given functions of <em>f </em>and <em>g</em>, where;
,
gives the domain of the functions as the option;
a. All non zero real numbers
<h3>How can the domain of the functions be found?</h3>
The given functions are presented as follows;
![f(x) = \frac{2}{ {x}^{2} }](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20%5Cfrac%7B2%7D%7B%20%7Bx%7D%5E%7B2%7D%20%7D%20%20)
![g(x) = \frac{13}{ {x}^{2} }](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%20%5Cfrac%7B13%7D%7B%20%7Bx%7D%5E%7B2%7D%20%7D%20)
The given functions have <em>x²</em> as the denominator, therefore;
The domain of the functions are the possible x-values, which gives;
x² = (-x)² = Positive number
At <em>x </em>= 0, we have;
![f(x) = \frac{2}{ {0}^{2} } = \infty](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20%5Cfrac%7B2%7D%7B%20%7B0%7D%5E%7B2%7D%20%7D%20%20%3D%20%20%5Cinfty%20)
![g(x) = \frac{13}{ {0}^{2} } = \infty](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%20%5Cfrac%7B13%7D%7B%20%7B0%7D%5E%7B2%7D%20%7D%20%20%3D%20%20%5Cinfty%20)
The domain is therefore;
a. All non zero real numbers
Learn more about the domain and range of a function here:
brainly.com/question/2264373
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