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- anonymous

find the domain and range of cos^-1(x^2-1)

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- anonymous

find the domain and range of cos^-1(x^2-1)

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- anonymous

range of cos ?

- anonymous

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

- anonymous

huh?

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- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

yes give me one second :)

- anonymous

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

- anonymous

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

- anonymous

nope

- anonymous

|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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

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