But I need help on this one now

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$What is the domain of the function $$f(t) = \frac{1}{(t-1)^2+(t+1)^2}~?$$ Express your answer in interval notation.$

Guest Nov 9, 2014

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Best Answer

+130511

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This function will be undefined wherever the denominator = 0

So, setting (r - 1)^2 + (r + 1)^2 = 0 (and expanding) we have

r^2 - 2r + 1 + r^2 + 2r + 1 = 0

2r^2 + 2 = 0 divide through by 2

r^2 + 1 = 0

And this never = 0

So this is defined everywhere, i.e., ( -∞, ∞ )

CPhill Nov 9, 2014

1⁺⁰ Answers

+130511

+5

Best Answer

This function will be undefined wherever the denominator = 0

So, setting (r - 1)^2 + (r + 1)^2 = 0 (and expanding) we have

r^2 - 2r + 1 + r^2 + 2r + 1 = 0

2r^2 + 2 = 0 divide through by 2

r^2 + 1 = 0

And this never = 0

So this is defined everywhere, i.e., ( -∞, ∞ )

CPhill Nov 9, 2014

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