Chapter A.3, Problem 18E

Solution

Find the domain of the algebraic expression.

Domain: $(-\infty ,-1)\cup (-1,\infty )$

Given:

The given algebraic expression is $x{(x+1)}^{-2}$ .

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 $x{(x+1)}^{-2}=\frac{x}{{(x+1)}^2}$ .

The Domain of $\frac{x}{{(x+1)}^2}$ is−

  $\begin{array}{c}x+1\ne 0\\ x\ne -1\end{array}$

So Domain is $x<-1orx>-1$

Domain: $(-\infty ,-1)\cup (-1,\infty )$