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Draw the graph of y=cos^(-1){x}," where ...

Draw the graph of `y=cos^(-1){x}," where "{*}" represetns the fractional part function"`.

Text Solution

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We have `y=cos^(-1){x}`
`{x}in[0,1)AAx in R`
Hence the domain of the function is R.
`0le{x}lt1`
`:." "0ltcos^(-1){x}lepi//2`
So the range of `y=f(x)is (0,pi//2]`
Now y=f(x) is periodic and has period '1'.
Also for `0lexlt1, {x}=x:.ycos^(-1){x}=cos^(-1)x` Graph of `y=|x|=x" and "cos^(-1){x}=cos^(-1)x`
Graph of `y={x}=x" and "y=cos^(-1){x}=cos^(-1)"x for x"in[0,1)" is shwon in the following figure".`

Since, the peirod of `y=f(x) is 'I'`, the graph of the function can be drawn by repeating the above for each interval `(n, n+1)n in Z`.
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