Question #129e0

1 Answer
Sep 7, 2015

(-#oo#,#oo#) ; (#-oo#, 1)#uu#(1,#oo#) ; #[#-2,#oo#)

Explanation:

The domain of an equation is the possible numbers on the denominator that allow the equation to make sense - making sure you never divide by zero.

Therefore we need to look at where the denominator may equal 0.
#x^2# + 5 = 0. Start off by solving by zero
#x^2# = -5 Then take the square root
#x# = #sqrt(-5)# This is impossible therefore the Domain is all real numbers or (-#oo#,#oo#)

Lets do the same thing again
#x#-1 = 0 Solve for zero
#x# = 1 This is the solution where x equals 0, remember x can never be equal to the solution so we have to exclude it from the domain.
Therefor #x# can be any number as long as its not 1.

The last equation is a square root so we know it can never be negative. The only numbers that can make the square root negative is from -3 to -#oo# therefore we can go up to and include -2 in our domain therefore: #[#-2,#oo#)