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)