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Let F : R+ → R, Where R+ Is the Set of All Positive Real Numbers, Such That F(X) = Loge X. Determine(C) Whether F(Xy) = F(X) : F(Y) Holds - Mathematics

Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine

(c) whether f(xy) = f(x) : f(y) holds

 
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Solution

Given:
f : R+ → R
and (x) = logex .............(i)

(c) (xy) = loge(xy)      {From(i)}
         = logex + logey         [Since logemn = loge m + logen]  
         = f (x) + f (y)
Thus, f (xy) = f (x) + f (y)
Hence, it is clear that f (xy) = (x) + f (y) holds.

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 3 Functions
Exercise 3.1 | Q 7.3 | Page 7
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