Which of the following function/functions has/have point of inflection? `f(x)=x^(6/7)` (b) `f(x)=x^6` `f(x)=cosx+2x` (d) `f(x)=x|x|`

Explanation

`f:Z to Z ,f(x) = x+2` is both one-one and onto.
Hence invertible.
`f:Z to Z ,f(x) = 2x` is one-one but not onto as range is set
`{…,-4,-2,0,2,4,6, …}`. Hence not invertible.
`f:Z to Z ,f(x) = x` is one-one and onto, Hence invertible.
`f:Z to Z ,f(x) = |x|` is many-one, Also, range is
`{0,1,2,3,...}`, So, into, Hence not invertible.