Solve this: 12 Of f:R→S defined by fx=sinx-3 cos x+1 is onto, then the interval of S - Maths - Relations and Functions

Question

Solve this:

12   Of   f : R → S   defined   by  
f x = sinx - 3   cos   x + 1   is   onto ,
  then   the   interval   of   S   is
A   - 1 , 3              
          B     1 , 1 C   0
, 1                  
            D   0 , - 1

Aarushi Mishra · Accepted Answer

fx=sin x-3 cos x+1=212sin x-32 cos x+1=2sin x cos π3-sin π3 cos x+1=2 sin x-π3 +1Since -1≤sin θ≤1-1≤sin x-π3≤1-2≤2 sin x-π3≤2-2+1≤2 sin x-π3+1≤2+1-1≤2 sin x-π3+1≤3-1≤fx≤3S=-1, 3

Solve this: 12 . Of f : R → S defined by f x = sinx - 3 cos x + 1 is onto , then the interval of S is . A - 1 , 3 B 1 , 1 C 0 , 1 D 0 , - 1

Solve this:

$12 . Of f : R \to S defined by f (x) = sinx - \sqrt{3} \cos x + 1 is onto, then the interval of S is . (A) [- 1, 3] (B) [1, 1] (C) [0, 1] (D) [0, - 1]$