Q. 35.0( 2 Votes )

Mark the correct alternative in each of the following:

If f : A B given by 3f(x) + 2–x = 4 is a bijection, then

A. A = {x ϵ R : –1 < x < ∞}, B = {x ϵ R : 2 < x < 4}

B. A = {x ϵ R : –3 < x < ∞}, B = {x ϵ R : 0 < x < 4}

C. A = {x ϵR : –2 < x < ∞}, B = {x ϵ R : 0 < x < 4}

D. none of these

Answer :

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


3f(x) + 2–x = 4


3f(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.

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