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What is the domain and range of #g(t)= sqrt(1-2^t)#?

Answer 1

Eva Adamson

Domain: #(-oo, 0]#
Range: #[0, 1]#

Domain: t can take on values from #0# and all negative real numbers.

Range #g(t)# can take values from #0# to #1#.

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Answer 2

Jace Anderson

The domain of the function g(t) = sqrt(1 - 2^t) is all real numbers t such that 1 - 2^t is non-negative, which means (1 - 2^t \geq 0). Solving this inequality gives (t \leq 0). Therefore, the domain of g(t) is all real numbers (t \leq 0).

The range of the function g(t) = sqrt(1 - 2^t) depends on the behavior of the expression inside the square root. Since (1 - 2^t) is always non-negative for (t \leq 0), the square root of (1 - 2^t) will always be a non-negative real number. Therefore, the range of g(t) is all non-negative real numbers.

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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.