Question

If f(x) be a function such that 2f(x)+f(-x)=cos x for every real number x.Then find the value of f(pi)​

Answer 1

Answer:

f(π)= -1/3

Step-by-step explanation:

substitute x with -x

2f(x) + f(-x)= cosx

2f(-x) + f(x)= cosx

f(x)=cosx/3 after solvinfg the above eqn

f(π)= -1/3

Answer 2

Answer:

$f(\pi ) = -\frac{1}{3}$

Step-by-step explanation:

According to the question ,  f(x) be a function such that 2f(x)+f(-x)=cos x for every real number x.

$2f(x)+f(-x)=cos x$..........(i)

x is replaced by -x.

$2f(-x)+f(x)=cos x$...........(ii)

(i)*2 - (ii)

$4f(x)+2f(-x)-2f(-x)-f(x)=2cos x-cosx\\\\or , 3f(x) = cos x\\\\or , f(x)=\frac{cos x}{3}$

$So , f(\pi ) = \frac{cos \pi }{3} = -\frac{1}{3}$

#SPJ3