Can someone explain how to find the domain of this?
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The domain of the square root function is non-negative real numbers. That gives us this restriction:
e^t - 1 ≥ 0
e^t ≥ 1
t ≥ 0
The argument of the square root is e^t - t, which is real for all real t, so there are no other restrictions. This is the domain:
t ≥ 0
e^t - 1 ≥ 0
e^t ≥ 1
t ≥ 0
The argument of the square root is e^t - t, which is real for all real t, so there are no other restrictions. This is the domain:
t ≥ 0
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You can simply draw the graph of this function and you'll find that t>0 is the domain of this function.
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We have to consider that we can't find the square root of a negative in the real numbers so e^t - 1 >0
e^t > 1
t > ln1
t > 0
e^t > 1
t > ln1
t > 0