1.

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

Answer»

(0,1)
`(-oo,1)`
(-1,1)
`(1,oo)`

Solution :`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`


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