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Draw the graph of y=cos^(-1)x^(3)" and c...

Draw the graph of `y=cos^(-1)x^(3)" and compare with the graph of "y=cos^(-1)x.`

Text Solution

Verified by Experts

We have `y=f(x)=cos^(-1)x^(3)`
We must have `-1lex^(3)le1therefore-1lexle1`
Also `cos^(-1)x^(3)` is decreasing as `cos^(-1)x` is decreasing and `x^(3)` is increasing
`f(-1)=cos^(-1)(-1)^(3)=cos^(-1)(-1)=pi`
`f(0)=cos^(-1)1=0`
`f(1)=cos^(-1)1=0`
For `-1lexlt0, xltx^(3)thereforecos^(-1)x^(3)," hence the graph of y="cos^(-1)x^(3)" line above the graph of y="cos^(-1)x.`
For `-1lexlt0, xltx^(3):.cos^(-1)x^(3)ltcos^(-1)x^(3),"hence the graph of y="cos^(-1)x^(3)"line below the praph of y="cos^(-1)x.`
Therefore, the graphs of both functions are as show in the following figure.
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