1. ## Range of a radical function

Hi everyone, I'm new here. I would appreciate it if someone can help me with this question. I need to find the range of the following function f(x) = (3x-2)^(1/2009). Thanks for any help

2. Let $g(x)=\sqrt[2009]{x}, \ h(x)=3x-2$.

Then $f(x)=\sqrt[2009]{3x-2}=g(h(x))$.

g and h are continuous and strictly increasing, so f is continuous and strictly increasing.

$\lim_{x\to-\infty}f(x)=-\infty, \ \lim_{x\to\infty}f(x)=\infty$.

Then the range of f is $\mathbb{R}$ (the set of real numbers).

3. Thank you so much, I was a bit confused with the graph of the function, it made it seem like the range was from -1 to 1, but it's just that the function is increasing very slowly. Thanks again!