range of f(x)= log x + sin x

[apple2357]

I am pretty sure the domain of this function is x>0. However i am not sure about the range of this function.
Sketching it , it looks like it all it might have a minimum value though i am not sure how to work it out.

 

[MarkFL]

What is the limit of the function at the domain boundaries? Is the function continuous?

 

[Dr.Peterson]

You can't determine domain and range just from looking at a piece of graph. It might do just about anything beyond what you show here.

Most important, there is no indication whether it is bounded for large x, and no basis for expecting any particular bound. Zooming out would give some reason to think it continues as we see here, but we would still not be certain.

Do you have the function itself??

 

[Deleted member 4993]

You can't determine domain and range just from looking at a piece of graph. It might do just about anything beyond what you show here.

Most important, there is no indication whether it is bounded for large x, and no basis for expecting any particular bound. Zooming out would give some reason to think it continues as we see here, but we would still not be certain.

Do you have the function itself??

S/he did state in the title:
f(x)= log x + sin x

 

[apple2357]

What is the limit of the function at the domain boundaries? Is the function continuous?

Not sure how i could work out the lim of f(x) = log x ( or ln x if it makes it easier) + sinx as x tends towards zero.. i was thinking expansions but lnx doesn't have one.

 

[MarkFL]

Not sure how i could work out the lim of f(x) = log x ( or ln x if it makes it easier) + sinx as x tends towards zero.. i was thinking expansions but lnx doesn't have one.

I would simply informally state:

[MATH]\lim_{x\to-\infty}e^x=0\implies \lim_{x\to0}\log(x)=-\infty[/MATH]

 

[apple2357]

I would simply informally state:

[MATH]\lim_{x\to-\infty}e^x=0\implies \lim_{x\to0}\log(x)=-\infty[/MATH]

But the graph above suggests that the limit of log(x)+sin(x) as x tends towards zero is not undefined?

 

[pka]

S/he did state in the title: f(x)= log x + sin x

Given that function

Not sure how i could work out the lim of f(x) = log x ( or ln x if it makes it easier) + sinx as x tends towards zero.. i was thinking expansions but lnx doesn't have one.

If you know that \(\displaystyle \mathop {\lim }\limits_{x \to \infty } \log (x) = \infty \), what do you say about \(\displaystyle \mathop {\lim }\limits_{x \to \infty } \log (x) +\sin(x)= ~? \)

 

[MarkFL]

But the graph above suggests that the limit of log(x)+sin(x) as x tends towards zero is not undefined?

Graphs can be misleading sometimes.

 

[apple2357]

 

[Steven G]

I am pretty sure the domain of this function is x>0. However i am not sure about the range of this function.
Sketching it , it looks like it all it might have a minimum value though i am not sure how to work it out.
View attachment 11805

You should know that the range of ln(x) is all real numbers. Now all the sin(x) graph is going to add a value between -1 and 1 to the ln(x) graph. The range is still all real numbers. This is only true since both functions are continuous on its domain.