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How do you find the domain and range of #ln(14t)#?

Answer 1

Domain: #x in RR^+#
Range: #y in RR#

The #ln# function is not defined for values less than or equal to #0#, so we can say that the domain is the positive real numbers, #RR^+#.

The range is a bit tricky. If you were looking at a graph of the function, you might think that you see a horizontal asymptote, but it actually isn't. It is just the fact that the #ln()# function is increasing so slow that it seems to be approach some value, but if you look at the values as they go towards infinity, there is no bound.

You can use a bit of calculus to make this extra clear. If you look a the following limit,

#lim_(x->oo)ln(14x)=oo#

it becomes quite clear that there is no bound and therefor no asymptote. This means that the range is all real numbers, #RR#.

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Answer 2

Eva Adamson

The domain of ln(14t) is all positive real numbers greater than 0, since the natural logarithm function is only defined for positive real numbers. The range of ln(14t) is all 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.