Question

Question #129e0

Answer 1

(-`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`)