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Let f : R rarr R be such that f is inj...

Let f : `R rarr R` be such that f is injective and `f(x) f(y ) = f(x+ y)forall x,y in` R. If f(x),f(y),f(z)are in G .P.,then x, y, z are in

A

A.P. always

B

G.P. always

C

A.P. depending on the values of x, y, z

D

G.P. depending on the values of x, y, z

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • Let f : R to R be a function given by f(x+y) = f(x) + f(y) for all x,y in R such that f(1)= a Then, f (x)=

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    f(x) is an odd function, if `f(0) ne 0`
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