The range of the function t-->ln t defined for all positive numbers is: Solution

Question

The range of the function t-->ln t defined for all positive numbers is:

Explanation / Answer

First, the domain of cos(t) is all real numbers the range is [ -1, +1 ] The domain of ln(x) is all real numbers > 0 as ln(x) is not defined for numbers less than or equal to 0 for g(t) = ln(cos(t)) as the cos function is embedded in the ln function, the range of the cos function becomes the domain of the ln function the cos function range is [ -1, +1 ] but we have to shrink that down to ( 0, +1 ] Now we have to figure out the domain from that range, as we are no longer able to use all the real numbers. The cos function is a repeating function, and for its range to be (0,+1] that means the domain must be only numbers in half of that function. I could explain this better with a graph. The domain will end up being -90 degrees

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