Find the inverse of the function: `f:[-1,1]rarr[-1,1]` defined by`f(x)=x|x|`

Answer

`f^(-1)(x)={(-sqrt(-x)",",x lt 0),(sqrt(x)",",x ge 0):}`

Explanation

`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):}`