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CGP EDU Academic Team
Published on: August 14, 2026
Let g : R → (0, π /3] is defined by g(x) = cos –1 
. Then find the possible values of ‘k’ for which g is surjective.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
k = – 
Sol. For g(x) to be surjective x ∈ R ⇒ 0 < cos –1 
< π /3 ⇒ 
< 
< 1
x 2 + 1 > 0 
x ∈ R
(x 2 + 1) < x 2 – k < x 2 + 1 ....(1)
From Eq. (1), taking RHS
x 2 – k < x 2 + 1 ⇒ k > –1
From Eq. (1), taking LHS
x 2 + 1 < 2x 2 – 2k ⇒ x 2 > 2k + 1 
x ∈ R
2k + 1 < 0 ⇒ k < 
⇒ k ∈ 
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