consider the function f(X) =x+cosx -a
values of a for which f(X) =0 has exactly one negative root are

Options

A. (0,1)
B. `(-oo,1)`
C. (-1,1)
D. `(1,oo)`

Answer

2

Explanation

`f(x)=x+cosx-a or f(X)=1 -sinx ge 0 forall x in R`
Thus f(X) is increasing in `(-oo,oo)` as for f(x) =0 x is not forming an interval also
f(X) =-cos x =0
or `x =(2n+1)(pi)/(2),nin Z`
Hence there are infinite points of inflection
Now f(x) =1-a
For positive root `1-alt0 or agt1` for negative root `1-agt 0 or a lt1`