Mark the correct alternative in each of the following: If f : A → B given by 3 f(x) + 2 –x = 4 is a bijection, then

Question

Philoid · Accepted Answer

Given that f: A → B given by 3^f(x) + 2^–x = 4 is a bijection.

3^f(x) + 2^–x = 4

⇒ 3^f(x) = 4 - 2^–x

⇒ 4 - 2^–x ≥ 0

⇒ 4 ≥ 2^–x

⇒ 2 ≥ -x

⇒ x ≥ -2

So, x ϵ (-2, ∞)

But, for x =0, f(x) = 1.

Hence, the correct option is none of these.