anonymous
  • anonymous
find the domain and range of cos^-1(x^2-1)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
range of cos ?
anonymous
  • anonymous
i mean what's the max and min of cos x?
anonymous
  • anonymous
huh?

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anonymous
  • 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
  • anonymous
and yoru range is between 0 and pi (so 0<=y<=pi)
anonymous
  • anonymous
and for hte domain it is - sqrt(2) <=x<=sqrt(2)
anonymous
  • anonymous
@MarcLeclair may you please show me how to do it?
anonymous
  • anonymous
yes give me one second :)
anonymous
  • anonymous
did your teacher giove you the domain of the arccosine function?
anonymous
  • anonymous
There is a set one but im just wondering if you have it
anonymous
  • anonymous
nope
anonymous
  • 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
  • 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
  • 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
  • anonymous
hope it helped if you need help wit hthe inequalities I will :)
anonymous
  • anonymous
0<= arccosin (x^2+1)<=pi*

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