The range of the function `f(x)=(x^2+x+2)/(x^2+x+1),x in R ,` is

Options

A. `(1, oo)`
B. `(1, 11//7]`
C. `[1, 7//3]`
D. `(1, 7//5]`

Answer

C

Explanation

Clearly, f(x) is defined for all `x in R`
So, domain (f) = R. Let f(x) = y Then,
`(x^(2) +x +2)/(x^(2) + x +1) = y`
`rArr x^(2) (y-1) + (y-2) ge 0`
Also, `y ne 1` for any `x in R`. Hence range of `f(x) = [1,7//3]`