Find the complete set of values of `alpha`for which the function
f(x) =`{(x+1,xlt1`
`alpha`, x =1 , is strictly increasing x=1
`x^(2)-x+3,xlt1`

Explanation

x+1 is increasing function.
Also `(d)/(dx)(x^(2)-x+3)=2x-1 gt 0 "for" x gt 1`
`therefore x^(2)-x+1` is increasing functions for `x gt 1`

Hence f(x) is increasing functions at x=1
if `lim (x+1)le lambda (x^(2)-x+3)`
`therefore 2 le lambda 3`