## virtus 3 years ago find the domain and range of cos^-1(x^2-1)

1. akash123

range of cos ?

2. akash123

i mean what's the max and min of cos x?

3. virtus

huh?

4. MarcLeclair

I think hes asking if its asked for an interval or the whole function. Because if there are no interval than the domain of cosine is for all real numbers

5. MarcLeclair

and yoru range is between 0 and pi (so 0<=y<=pi)

6. MarcLeclair

and for hte domain it is - sqrt(2) <=x<=sqrt(2)

7. virtus

@MarcLeclair may you please show me how to do it?

8. MarcLeclair

yes give me one second :)

9. MarcLeclair

did your teacher giove you the domain of the arccosine function?

10. MarcLeclair

There is a set one but im just wondering if you have it

11. virtus

nope

12. MarcLeclair

|dw:1347453496255:dw|Okay so the arccosine function has ( INITIALLY) a domain of -1<=x<=1 and a range of 0<=y<=pi this is because the graph of a arccos is mor vertical, if we ake a range or domain bigger than that it loses its role of function as one x has more than one image

13. MarcLeclair

however, the function youve asked for has been shifted. Therefore, you have to solve for not arccosine X but arcossine x^2-1. for the domain you do as follow -1<= (x^2+1)<= 1

14. MarcLeclair

same goes for the range, you hae 0<=y<=pi, then you have to insert your function so : 0<= arccosin (x^2+1)<=0 You then have to solve forthe inequality :D

15. MarcLeclair

hope it helped if you need help wit hthe inequalities I will :)

16. MarcLeclair

0<= arccosin (x^2+1)<=pi*