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What is the domain and range of #y(x)=ln(x+2)#?

Answer 1

Julia Adams

The domain is #x in (-2, +oo)#.
The range is # y in RR#

What's in the log function is #>0#

Consequently,

#x+2 >0#

#x > -2#

The domain is #x in (-2, +oo)#

Let #y=ln(x+2)#

#x+2=e^y#

#x=e^y-2#

#AA y in RR, e^y>0#

The range is # y in RR#

plot{ln(x+2) [-8.54, 23.5, -9.32, 6.7]}

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Answer 2

Ethan Adkins

The domain of the function ( y(x) = \ln(x+2) ) is all real numbers greater than -2, since the natural logarithm function is defined only for positive real numbers. Therefore, the domain is ( x \in (-2, \infty) ).

The range of the function is all real numbers, since the natural logarithm function can output any real number as its value. Therefore, the range is ( y \in (-\infty, \infty) ).

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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.