Question

Show that f(x)= x2 + cos x, is an even function.

Answer 1

Given :   f(x) = x²  + cosx

To find :  Function is even

Solution:

Even Function

if f(x) = f(-x)

f(x) = x²  + cosx

f(-x) = (-x)² + cos(-x)

(-x)²  =  x²   &   cos(-x) =  Cosx

=> f(-x) = x²  + cosx

=>  f(-x)  = f(x)

Hence f(x) = x²  + cosx is an even function

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