Inverse Trig Question (1 Viewer)

[rand_althor]

Hey could someone help me with finding the range and domain of:



Also how would I graph the function?

Thanks!

 

[leehuan]

The x part doesn't affect the domain, since y=x exists for all real x.



I think graphing that would be a bit out of the ordinary for 3U... I'd use the 4U method of multiplying ordinates.

 

[integral95]

It's an odd function

well compared to the typical inverse sine function your graph would be much lower than that in the domain



Once you get that part, use the property that it's an odd function to sketch the left hand side.

 

[Cheefi]

What is the range?

 

[InteGrand]

What is the range?

The range is .

Here's a useful sketch: http://www.graphsketch.com/?eqn1_co..._lines=1&line_width=4&image_w=850&image_h=525

 

[Cheefi]

Is it possible to find the range without sketching the function?

 

[InteGrand]

Is it possible to find the range without sketching the function?

Yes; the function is clearly monotonically increasing on [0, 1], as it is the product of two monotonically increasing non-negative functions ( and ), and f is an odd function, so the extreme values of the function just occur at the endpoints of the domain.