Let f: R arrow[0, (π/2)) be defined by f(x)= tan -1(3 x2+6 x+a). If f(x) is an onto function then the value of a is

Question

Let f: R arrow[0, (π/2)) be defined by f(x)= tan -1(3 x2+6 x+a). If f(x) is an onto function then the value of a is (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

The equation 3 x2+6 x+a=0 must have equal roots text So, D=0 ⇒ 36-12 a=0 ⇒ a=3

Q. Let $f : R \to [0, \frac{π}{2})$ be defined by $f (x) = tan^{- 1} (3 x^{2} + 6 x + a)$ . If $f (x)$ is an onto function then the value of $a$ is