Question

Let f : R → [ 2 , ∞ ) be a function defined as f ( x ) = x² − 12 ax + 15 − 2 a + 36a² . If f ( x ) is surjective on R, then the value of a is

Answer 1

Rewriting the given function, we get,

f(x) = (x - 6a)² + 15 - 2a

\(\because\) f (x) is surjective on R 

⇒ 15 - 2a = 2 

⇒ 2a = 13 

⇒ a = 13/2