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Let f : (-infty,1] rarr (-infty, 1] such...

Let f : `(-infty,1] rarr (-infty, 1]` such that f(x) = x(2 -x), then `f^-1 (x)` is

A

`1 + sqrt(1 -x)`

B

`1 - sqrt(1 -x)`

C

`sqrt(1 -x)`

D

` sqrt(1 +x)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `y = x(2 - x) rArr x^2 - 2x + y = 0 rArr (x - 1)^2 = 1-y rArr x = 1 +- sqrt(1 - y)`
But, `x ge 1`, so, x = 1 - sqrt(1 - y) = t^-1 (y)`
Hence, `f^-1(x) = 1 - sqrt(1 - x)`
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