Question

What is the domain and range of f(x)=2^x+1

Answer 1

domain all real numbers. you can raise 2 to any power

Answer 2

range is
\[(1,\infty)\] because 2 to any power is positive

Answer 3

and since
\[2^x>0\] then
\[2^x+1>1\]

Answer 4

Sorry - I wasn't looking at my computer. I had the domain as all real numbers. So the range would be written as 2^x+1>1?

Answer 5

\[D=\mathbb{R} \]
\[\lim_{x \rightarrow +\infty}f(x)=+\infty , \ \lim_{x \rightarrow -\infty} f(x)=\]
\[f:\mathbb{R} \rightarrow ]1;+\infty[\]

Answer 6

Sorry,
\[\lim_{x \rightarrow -\infty}f(x)=1\]

Answer 7

range is usually written just as an interval but you could write
\[2^x+1>1\] if you like

Answer 8

Thanks someone 1348....this answer looks very difficult. Is there a more simple way?

Answer 9

I don't think that would look good.

And my answer isn't difficult :p it just looks like it is.
It just means,
Domain is R, meaning the function is defined for all real numbers
since f is strictly increasing, we can use the limits to find the range of the function, meaning we'll find the lowest and highest value... However since they're limits and the function doesn't really *get* to those values, we have to use open intervals.
We can therefore conclude that f is a function of the set of real numbers into the interval of all real numbers greater than, but not equal to, 1.

Answer 10

Can I say 2^+1>1 is the range?

Answer 11

So, if I write it out I can say the range is the set of real numbers greater than, but not equal to one.

Answer 12

I wouldn't use an inequality to write a range, it doesn't look like proper math, you should use interval notation.
And yes you could write it out like that.

Answer 13

OK. This is a basic algebra class and my instructor's notes don't show intervals just simple sentences. So for this one, I think my answer of "all real numbers greater than, but not equal to one is the range for f(x)=2^x+1.

Thank you for your help.