Question

True or False The domain of the function $f\left(x\right)=\frac{x^2-4}{x}$is$\left\{x\right|x\ne \pm 2\}$.

Short answer

The given statement is false.

Step-by-step solution

Step 1. Given information 

In the given question we have to explain the given statement is true or false.

The statement is "The domain of the function $f\left(x\right)=\frac{x^2-4}{x}$is $\left\{x\right|x\ne \pm 2\}$."

Step 2. The given function is f(x)=x2-4x.Finding the domain of function.

The given function tells us to divide $x^2-4$by $x$. Since division by $0$is not defined, the denominator $x$can never be $0$, so $x$can never equal $0$.

Step 3. The domain of the given function is {x|x≠0}

Hence, the given statement is false.