NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

If f x = t a n - 1 x 2 + 4 x + s i n - 1 x 2 + 4 x + 1 , then

Options

Adomain of f x contains 3 integers only
Brange of f x has two elements only
Cf x is a constant function ∀ x ∈ R
Df x contains only two elements in its domain

Correct answer

D. f x contains only two elements in its domain

Step-by-step solution

∵   x 2 + 4 x ≥ 0 for the first term and 0 ≤ x 2 + 4 x + 1 ≤ 1 for the second term ∴ by both the results, there is only one possibility x 2 + 4 x = 0 ⇒ x = 0 , - 4 ∴   f x = tan - 1 ⁡ 0 + sin - 1 ⁡ 1 = π 2

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