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How do you find the domain of f(x)=arcscos(e^x) ?? The answer is (-infinity, 0] but I don't understand why!?
Update:
arccos(e^x) **
1 Answer
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- PopeLv 74 years ago
The domain of the arccos function is [-1, 1].
In the function arccos(e^x), the argument of the arccos function is e^x. It must be on the domain above.
-1 ≤ e^x ≤ 1
But e^x is positive for all real x, so reject the non-positive part of the interval.
0 < e^x ≤ 1
lim e^x < e^x ≤ e^0
x→-∞
-∞ < x ≤ 0
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