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Question: If \(f(y) = \log y,\) then \(f(y) + f\left( \frac{1}{y} \right)\) is equal to...

If f(y)=log⁡y,f(y) = \log y, then f(y)+f(1y)f(y) + f\left( \frac{1}{y} \right) is equal to

A

2

B

1

C

0

D

– 1

Answer

0

Explanation

Solution

Given f(y)=log⁡y⇒f(1/y)=log⁡(1/y)f(y) = \log y \Rightarrow f(1/y) = \log(1/y), then f(y)+f(1y)f ( y ) + f \left( \frac { 1 } { y } \right)

=log⁡y+log⁡(1/y)=log⁡1== \log y + \log(1/y) = \log 1 =0.