Let f : R → [0, π/2) (where R is the set of real numbers) be a function defined by $f(x)=\tan^{-1}(x^2+x+a)$. If f is onto then a equals
Answer & explanation
Correct answer: option 4
F is onto ⇒ Range of f is [0, π/2) ⇒ $0 ≤ x^2 + x + a < ∞, ∀\, x ∈ R$
$⇒ 0 ≤ \left(x+\frac{1}{2}\right)^2+a-\frac{1}{4}< ∞,\,∀\, x ∈ R⇒a=1/4$