The least integral value of `x` where `f(x)=(log)_(1/2)(x^2-2x-3)` is monotonically decreasing is________

Answer

4

Explanation

`x^(2)-2x3gt0`
or `(x-3)(x+1)gt0`
i.e `xlt1 or xgt3`
Now `f(X)=log_(1//2)(x^(2)-2x-3)`
`=log_(e)(x^(2)-2x-3)/(log_(e)(1//2))`
`f(X)=(2x-2)/(log_(e)(1//2))(x^(2)-2x-3)`
For f(x) to decreasing `f(X)lt0`
or `(x-1)/(log_(e)(1//2)(x-3)(x+1))lt0`
or `xgt1`
From 1 and 2 x `gt`3