Question

The range of f(x) = cos [x], for -π/2< x <π/2 is

A. {-1,1,0} 

B. {cos 1, cos 2,1} 

C. {cos 1, -cos 1,1} 

D. [-1,1]

Answer 1

Option : (B)

Given,

f(x) = cos [x], for -π/2< x <π/2

For -π/2< x <-1,

[x]= -2 

f(x)= cos[x]= cos(-2) 

= cos2 

Because,

cos(-x) = cos(x) 

For-1 ≤x<0 

[x] = -1 

f(x) = cos[x] 

=cos(-1) 

= cos1 

For 0 ≤x< 1,

[x] = 0 

f(x) = cos 0 

= 1

For 1≤ x <π/2,

[x] = 1 

f(x) = cos 1 

Therefore, 

R(f) = {1, cos 1,cos 2} 

Option B is correct.