NTA Abhyas JEE Main2020MathematicsFunctionsPractice

If f : R → 0 , π 2 , f x = s i n - 1 40 x 2 + x + λ is a surjective function, then the value of λ is equal to

Correct answer

40.25

Step-by-step solution

For f x to be surjective, 0 < 40 x 2 + x + λ ≤ 1 ⇒ ∞ > x 2 + x + λ 40 ≥ 1 Now, x 2 + x + λ ≥ 40 x 2 + x + λ = x 2 + x + 1 4 + λ - 1 4 = x + 1 2 2 + λ - 1 4 Now, for x 2 + x + λ to be minimum 40 λ - 1 4 = 40 ⇒ λ = 40.2 5

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