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Find the inverse of the function: f : [ ...

Find the inverse of the function: `f : [ − 1 , 1 ] → [ − 1 , 1 ] is defined by f ( x ) = x | x |

Text Solution

Verified by Experts

The correct Answer is:
`f^(-1)(x)={(-sqrt(-x)",",x lt 0),(sqrt(x)",",x ge 0):}`
`f:[-1,1] to [-1,1]` is defined by
`f(x)=x|x|={(x^(2)",",x ge 0),(-x^(2)",",x lt 0):}`
or `f^(-1)(x)={(sqrt(x)",",x ge 0),(-sqrt(-x)",",x lt 0):}`
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