Find the inverse of `f(x)={(x ,, x<1),(x^2 ,, 1lt=xlt=4), (8sqrt(x) ,, x >4):}`

Explanation

Given `f(x)={(x",", x lt1),(x^(2)",",1le x le 4),(8sqrt(x)",", x gt 4):}`
Let `f(x)=y`
or `x=f^(-1)(y) " (1) " `
` :. x={(y",", y lt1),(sqrt(y)",",1le sqrt(y) le 4),(y^(2)//64",", y^(2)//64 gt 4):}={(y",", y lt1),(sqrt(y)",",1le y le 16),(y^(2)//64",", y gt 16):},`
`f^(-1)(y)={(y",", y lt1),(sqrt(y)",",1le y le 16),(y^(2)//64",", y gt 16):}, " [From (1)]" `
Hence, `f^(-1)(y)={(x",", x lt1),(sqrt(x)",",1le x le 16),(x^(2)//64",", x gt 16):},`