Question

If $f\left(x\right)=\frac{x^2-x}{x^2+2x}$, then the domain of $f$ is

• A. $\left\{0,-2\right\}$
• B. $R-\left\{0,-2\right\}$
• C. $R$
• D. None of these

Answer 1

The correct option is B

$R-\left\{0,-2\right\}$

Explanation for the correct option:

Find the domain of function $f$:

A rational function is not defined at the values where its denominator is equal to zero.

So the function $f\left(x\right)=\frac{x^2-x}{x^2+2x}$ is not defined when $x^2+2x=0$.

$$\begin{gathered} x^2+2x=0 \\ \Rightarrow x\left(x+2\right)=0 \end{gathered}$$

So the function is not defined at $x=0$ and $x=-2$.

Thus the domain of the function $f\left(x\right)=\frac{x^2-x}{x^2+2x}$ is $R-\left\{0,-2\right\}$.

Hence, the correct option is B.