SOLUTION: indicate the domain: a(x)=(x+2)^-1

Question 386072: indicate the domain: a(x)=(x+2)^-1
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
When finding domains, you need to ensure that no numbers in the domain will make

a denominator zero
a radicand (expression within a radical) of an even-numbered root negative
a base or argument to a logarithm zero or negative
other "illegal" expressions (for example, )

Your function has no radicals or logarithms. And it may appear that it does not have a denominator. But if you understand what -1 as an exponent means then you will realize that we really do have a denominator:

So we have to make sure that the domain includes only numbers that make the denominator something other than zero. The way to determine this is to figure out what number(s) make the denominator zero and then exclude them from the domain. So we set the denominator equal to zero and solve:
x + 2 = 0
Subtract 2 from each side and we get:
x = -2
This is the only number that makes the denominator zero. So this is the only number we must exclude from the domain. So the domain is all real numbers except -2.
RELATED QUESTIONS
For each of the equations (a), (b), and (c) below, indicate which graphs represents the... (answered by Edwin McCravy)

find the domain of a function... (answered by Susan-math)

(1-x^2)/ x Find the domain (answered by josgarithmetic)

Solve the following and indicate the solution set: (1/x^2) * (x^2-x/x^2-1) + (2x-2/x+1) (answered by Susan-math)

Find the domain f(x)=... (answered by ikleyn)

1. The domain of function: f(x) = x-2 /... (answered by jim_thompson5910)

indicate the correct conic section for... (answered by lwsshak3)

what is the domain of (x-1)/(x^2+1) (answered by ewatrrr)

sketch the graph of {{{y=(1+x)^2}}} indicate the coordinates of important points... (answered by CubeyThePenguin)