Chapter 1.2, Problem 64E

To determine

To Find: the domain the function $h\left(x\right)=\frac{10}{x^2-2x}$ .

Answer to Problem 64E

Domain $=\left(-\infty ,0\right)\cup \left(0,2\right)\cup \left(2,\infty \right)$ .

Explanation of Solution

Given:

Given function is.

  $h\left(x\right)=\frac{10}{x^2-2x}$

Calculation:

If denominator will be zero then function will be undefined as $\frac{1}{x}=\infty$ therefore find the value of x at which function is undefined.

  $\begin{array}{l}{x}^2-2x=0\\ x\left(x-2\right)=0\\ x=0\text{ and }x-2=0\\ x=0\text{ and }x=2\end{array}$

Its domain is all real number except $x=0,2$ .

It can be written as Domain $=\left(-\infty ,0\right)\cup \left(0,2\right)\cup \left(2,\infty \right)$ .

Therefore, answer is Domain $=\left(-\infty ,0\right)\cup \left(0,2\right)\cup \left(2,\infty \right)$ .