Find the range of `f(x)=cos((log)_e{x})dot`

Answer

`[-1,1]`

Explanation

`f(x)=cos(log_(e){x}).`
For the given function to define,
`0 lt {x} lt 1`
or `-oo lt log_(e){x} lt 0`
For these values of `theta=(log_(e){x}, cos theta` takes its all possible values.
Hence, the range is `[-1,1].`