Mark the correct alternative in each of the following:
The function f : A → B defined by f(x) = –x2 + 6x – 8 is a bijection, if
Given that f: A → B defined by f(x) = –x2 + 6x – 8 is a bijection.
f(x) = –x2 + 6x – 8
⇒ f(x) = –(x2 - 6x + 8)
⇒ f(x) = - (x2 - 6x + 8 + 1 - 1)
⇒ f(x) = - (x2 - 6x + 9 - 1)
⇒ f(x) = - [(x – 3)2 – 1]
Hence, x ϵ (–∞, 5] and f(x) ϵ (–∞, 1]