Chapter A.3, Problem 16E

Solution

Find the domain of the algebraic expression.

Domain: $(-\infty ,0)\cup (0,2)\cup (2,\infty )$

Given:

The given algebraic expression is $\frac{3x-1}{x-2},x\ne 0$ .

Concept Used:

• A domain is the set of all possible input values for a function.
• To find the domain of a function, set the function equal to y and solve for x. This will give you the set of all x-values for which the function produces a real y-value.

Calculation:

The given algebraic expression is $\frac{3x-1}{x-2},x\ne 0$ .

The Domain of $\frac{3x-1}{x-2}$ is −

  $\begin{array}{c}x-2\ne 0\\ x\ne 2\end{array}$

And given that $x\ne 0$

So Domain is $x<2orx>2andx\ne 0$

Domain: $(-\infty ,0)\cup (0,2)\cup (2,\infty )$