Let f : RR be such that f(x) = 2 x . Determine:
(i) Range of f            (ii) {x : f(x) = 1}        (iii) whether f(x + y) = f(x) f(y) holds.

Dear Student,
Please find below the solution to the asked query:

fx=2xWe know that exponential function cannot be negative or 0.iHence range fo function is 0,ii x:fx=12x=12x=20x=0iiifx=2xfy=2yfx+y=2x+y=2x2y    As ax+y=axay=fxfyfx+y=fxfy holds 

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