# Thread: Exponentiation by an irrational number (short)

1. ## Exponentiation by an irrational number (short)

Hello my friends, I need help with this short problem.

Suppose f(x) = 3^x

1. Find all asymptotes of f.
2.Sketch the graph of f^-1 (f inverse) and label all asymptotes and important points
3. Estimate the value of x where f(x) = 24

Thanks

2. Originally Posted by goliath
Hello my friends, I need help with this short problem.

Suppose f(x) = 3^x

1. Find all asymptotes of f.
2.Sketch the graph of f^-1 (f inverse) and label all asymptotes and important points
3. Estimate the value of x where f(x) = 24

Thanks
Have you tried graphing the function as a starting point?

3. Yes, I have.

4. So where do you think the asymptotes are?

5. y=0?

6. Originally Posted by goliath
y=0?
Correct.

Now draw the inverse function (reflect $f(x)$ in the line $y = x$).

What is the inverse function? Where are its asymptotes and intercepts?

7. Is there a way to find the asymptotes without graphing? Or no?

8. Originally Posted by goliath
Is there a way to find the asymptotes without graphing? Or no?
If you know the basic properties of the logarithm function, then no, you don't need to graph.

9. Could you show me how to calculate asymptote?

10. I've already told you to graph $f(x)$, then reflect it in the line $y = x$.

Then the asymptotes become obvious.

Otherwise, do some research about logarithms.

11. gee, thanks..

12. You have a problem with that answer? He has already told you how to do that. He told you "If you know the basic properties of the exponential functions, then no, you don't need to graph." Clearly you do not or you would have realized immediately that there are no vertical asymptotes and that the only horizontal aysmptote is at x= 0. That was why he suggested graphing.

And the second part of the problem was to graph and find the asymptotes of the inverse function. The graph of the inverse function is the graph of the function itself reflected about the line y= x. And you can get its only asymptote from that.

13. Haha, no, I don't have a problem.