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Classify the following functions as inje...

Classify the following functions as injection, surjection or bijection. Find the inverse function if exists.
(i) `f: R-[2] to R-[1]` defined by `f(x) = (x-1)/(x-2)`
(ii) `f: R to R^(+)` defined by `f(x) = (1/2)^(x)`
(iii) `f : R to (0,1]` defined by `f(x) =1/(x^(2)+1)`

Text Solution

Verified by Experts

The correct Answer is:
(i) bijection; `f^(-1)(x) = (2x-1)/(x-1)`
(ii) bijection; `f^(-1)(x) = log_(1//2)x`
(iii) onto but non one-one
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