Let `f(x)` be an increasing function defined on `(0,oo)` . If `f(2a^2+a+1)>f(3a^2-4a+1),` then the possible integers in the range of `a` is/are (a)`1` (b) 2 (c) 3 (d) 4

Options

A. 1
B. 2
C. 3
D. 4

Answer

2,3,4

Explanation

Since f is defined on `(0,oo) ,2a^(2)+a+1gt0` which is true as
`Dlt0`
Also `3a^(2)-4a+1gt0`
`(3a-1)(a-1)gt0 i.e alt1//3 or agt1`
As f is increasing
`f(2a^(2)+a+1)gtf(3a^(2)-4a+1)`
or `2a^(2)+a+1gt3a^(2)-4a+1`
or `0gta^(2)-5a`
or `0gta^(2)-5a`
or `a(a-5)lt0 or a in (0,5)`
from (1) and (2) we get
`ain (0,1//3)cup(1,5)`
Therefore possible integers are {2,3,4}