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How do you find the domain of #p(t)=(t+9)/(t+3)#?

Answer 1

#t inRR,t!=-3#

Since equating the denominator to zero and solving for t yields the value that t cannot be, the denominator of p(t) cannot be zero as this would render p(t) undefined.

#"solve "t+3=0rArrt=-3larrcolor(red)" excluded value"#

#"domain is "t inRR,t!=-3#

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Answer 2

Hazel Anglin

To find the domain of ( p(t) = \frac{t+9}{t+3} ), we look for values of ( t ) that make the denominator zero because division by zero is undefined. Set the denominator equal to zero and solve for ( t ). In this case, ( t + 3 = 0 ), so ( t = -3 ). Therefore, the domain of ( p(t) ) is all real numbers except ( t = -3 ). In interval notation, the domain is ( (-\infty, -3) \cup (-3, \infty) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.