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

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The discussion focuses on determining the domains of the variables in two mathematical expressions. For the expression x + x^(-1), the domain is defined as all real numbers except zero, since x cannot equal zero. Similarly, for the expression t^(-1) + 2•t^(-2), the domain also excludes zero, as t cannot be zero. Participants clarify the correct interpretation of the second expression, emphasizing that the coefficient does not affect the variable's exponent. Overall, both expressions require that their respective variables cannot equal zero.
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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}
 
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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.
 
I rushed through the question.

In general, at^(-2) = a/t^2
 
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