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Numerade Educator

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Problem 20 Medium Difficulty

Find the domain of each function.

(a) $ g(t) = \sqrt{10^t - 100} $
(b) $ g(t) = \sin (e^t - 1) $

Answer

a) Domain : $[2,+\infty)$
b) $(-\infty, \infty)$

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Video Transcript

to find the domain of this function. Let's concentrate on the quantity inside the square root. We need that quantity to be greater than or equal to zero because that's the only way to get a really output. So we need 10 to the power t minus 100 to be greater than or equal to zero. So 10 to the power T is going to be greater than or equal to 100. Okay, we know that 10 to the second power is 100. So if t is greater than or equal to two, we ought to have numbers that will fit in the domain and will give us a real output. And if we want to put if we want to give this answer using interval notation, we can say to to infinity Now, for part B, we want to find the domain of this function. So if you think about it, the sine function in General Weichel sign of X has the domain, all real numbers. So it really doesn't matter what you end up getting for each of the T minus one. Because no matter what it is, it's going to be the sign of it is going to be riel and e to the T always gives you a real output. Subtracting one from that always gives you a real output on the sign of a real numbers. A real number. So there are no restrictions to the domain. The domain is going to be all real numbers, and you can write that as negative infinity to infinity.