## anonymous one year ago I need help in finding the range of the following function: arcsin(3x+1) For finding the domain I did the following... -1 </= 3x + 1 </= 1 then I solved both sides of the inequality separately to get -2/3 </= x </= 0 Please correct me if I'm wrong :) *by "</=" I mean "less than or equal to".

1. Vocaloid

yup, looks good to me! great job ~

2. anonymous

Great! Thanks @Vocaloid :) Ant ideas on how to find the range?

3. anonymous

Any*

4. Vocaloid

Hm, that's a bit trickier, I suppose you could evaluate arcsin(-2/3) and arcsin(0), but I'm sure there's a better way, let me think about this one for a second

5. anonymous

Alrighty! :D Thanks so much!

6. anonymous

I think the range of arcsin x is always -π/2 ≤ y ≤ π/2

7. anonymous

Wait would it be pi/2 - 3pi/2 ?

8. jim_thompson5910

I think you meant to say this for the domain $\Large -1 \le 3x{\color{red}+}1 \le 1$ and you solve for x from there

9. Vocaloid

yes, peachpi is right, silly me!

10. anonymous

@jim_thompson5910 you caught my typo again >.<

11. anonymous

@peachpi thank you!

12. jim_thompson5910

but you have the correct result after you isolate x $\Large -\frac{2}{3} \le x \le 0$ is the correct domain

13. anonymous

you're welcome

14. anonymous

@jim_thompson5910 okay so would be correct to find the range by just plugging in -2/3 and 0 ?

15. anonymous

*would it

16. jim_thompson5910

yep, plugging in x = -2/3 will give -pi/2 which is the lowest you can go in the range plugging in x = 0 will give pi/2 which is the highest you can go in the range