I need help in finding the range of the following function:
arcsin(3x+1)

For finding the domain I did the following...

-1

Question

I need help in finding the range of the following function: arcsin(3x+1) For finding the domain I did the following... -1

vocaloid · Answer

yup, looks good to me!

great job ~

anonymous · Answer

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

anonymous · Answer

Any*

vocaloid · Answer

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

anonymous · Answer

Alrighty! :D Thanks so much!

anonymous · Answer

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

anonymous · Answer

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

jim_thompson5910 · Answer

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

vocaloid · Answer

yes, peachpi is right, silly me!

anonymous · Answer

@jim_thompson5910 you caught my typo again >.<

anonymous · Answer

@peachpi thank you!

jim_thompson5910 · Answer

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

anonymous · Answer

you're welcome

anonymous · Answer

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

anonymous · Answer

*would it

jim_thompson5910 · Answer

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