FunctionHard
Question
The range of the function f (x) = sin-1 
+ cos-1
, where [ ] is the greatest integer function, is:
+ cos-1, where [ ] is the greatest integer function, is:Options
A.
B.
C.{π}
D.
Solution
f(x) = sin-1 
+ cos-1 
Domain : - 1 ≤
≤ 1 ⇒ x ∈ 
and - 1 ≤
≤ 1 ⇒ x ∈ 
⇒ domain is x ∈
or x2 ∈
if (i) x2 ∈
then f(x) = π
if (ii) x2 ∈
, then f(x) = π
if (iii) x2 ∈
, then f(x) = π ⇒ range = {π}
+ cos-1 Domain : - 1 ≤
≤ 1 ⇒ x ∈ and - 1 ≤
≤ 1 ⇒ x ∈ ⇒ domain is x ∈
or x2 ∈
if (i) x2 ∈
then f(x) = πif (ii) x2 ∈
, then f(x) = πif (iii) x2 ∈
, then f(x) = π ⇒ range = {π}Create a free account to view solution
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