First slide

Functions (XII)

Question

If f(x)=cos (log_ex),then the value of f(x)f(y)- $\frac{1}{2}$ $[f (\frac{x}{y}) + f (x y)]$ is

Moderate

A

-1
B

½
C

-2
D

none of these

Solution

Given,f(x)=cos(log_ex)
$∴$ f(x)f(y)- $\frac{1}{2}$ {f( $\frac{x}{y}$ )+f(xy)}
=cos (logx)cos (logy)- $\frac{1}{2}$ {cos log $|\frac{x}{y}|$ +cos log (xy)}
=cos (logx)cos( logy)- $\frac{1}{2}$ {cos (logx-logy)+cos (logx+log y)
=cos (logx)cos (logy)- $\frac{1}{2}$ {2cos (logx )cos (log y)}=0

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