MHB What is the domain of each variable in the given expressions?

[mathdad]

Specify the domain of each variable.

1. x + x^(-1)

I know that x^(-1) = 1/x.

So, x can be any number EXCEPT for 0.

Let D = domain

D = {x|x CANNOT be 0}

2. t^(-1) + 2•t^(-2)

Well, t^(-1) = 1/t.

Also, 2•t^(-2) = 1/2t^(2).

2t^2 = 0

t^2 = 0/2

t^2 = 0

sqrt{t^2} = sqrt{0}

t = 0

Let D = domain

D = {t|t CANNOT be 0}

 

[skeeter]

Also, 2•t^(-2) = 1/2t^(2)

fyi, $2t^{-2} = \dfrac{2}{t^2}$, not what you posted. Only $t$ is raised to the power of $-2$, not the coefficient, $2$.

yes, both expressions must exclude zero from the domain.

 

[mathdad]

I rushed through the question.

In general, at^(-2) = a/t^2