(i) Find whether `f(x)=x+cosx` is one-one.
(ii) Identify whether the function `f(x)=-x^(3)+3x^(2)-2x+4` for `f:RtoR` is ONTO or INTO
(iii) `f(x)=x^(2)-2x,[0,3]toA`. Find whether `f(x)` is injective or not. Also find the set A if `f(x)` is surjective

Explanation

(i) The domain of `f(x)` is `R` . `f'(x)=1-sinx`
`:. F'(x)ge0AAxepsilon` complete domain and equality holds at discrete points only
`:.f(x)` is strictly increasing on `R`. Hence `f(x)` is one-one.
(ii) As range `-=` codomain, therefore given function is ONTO
(iii) `f'(x)=2(x-1),0lexle3`

`:.f'(x)={{:(-ve,,,0lexlt1),(+ve,,,1ltxlt3):}`
`:. f(x)` is non monotonic. Hence it is not injective.
For `f(x)` to be surjective, A should be equal to its range. By graph range is `[-1,3]`
`:.A-=[-1,3]`