Q. 14 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

The given statement is false. 

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 ) = x 2 - 4 x . 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.