Question

Find the domain of the function. $$y=\frac{4}{x^{2}}$$

Short answer

The domain of the function \(y=\frac{4}{x^{2}}\) is all real numbers except x = 0, or in interval notation, \((-∞, 0) ∪ (0, ∞)\).

Step-by-step solution

Identify the Function

The given function is \(y=\frac{4}{x^{2}}\). Observe that there is a variable in the denominator.

Determine Where the Function is Undefined

A function is undefined when the denominator is equal to zero. Therefore, let's set the denominator equal to zero and solve for x: \(x^{2} = 0\). This gives one solution, x = 0.

Deduct the Undefined Point from the Real Numbers

The function is defined for all real numbers except for x = 0. So, the domain of the function \(y=\frac{4}{x^{2}}\) is all real numbers except x = 0. In interval notation, this can be written as \((-∞, 0) ∪ (0, ∞)\)