Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

The equation $3 x^2+6 x+a=0$ must have equal roots
$\text { So, } D=0 $
$\Rightarrow 36-12 a=0 \Rightarrow a=3$