Let `f(x)=a^(x)(a gt 0)` be written as `f(x)=f_(1)(x)+f_(2)(x), " where " f_(1)(x)` is an function and `f_(2)(x)` is an odd function. Then `f_(1)(x+y)+f_(1)(x-y)` equals

Let f (x) = a ^ x ( a gt 0 ) be written as f ( x ) = f _ 1 (x ) + f _ 2 (x) , where f _ 1 ( x ) is an even function and f _ 2 (x) is an odd function. Then f _ 1 ( x + y ) + f _ 1 ( x - y ) equals :

If f(x) is a function such that f(xy)=f(x)+f(y) and f(3)=1 then f(x)=

If f(x) is a function such that f(xy)=f(x)+f(y) and f(3)=1 then f(x) =

f(x+y)=f(x).f(y)AA x,y in R and f(x) is a differentiable function and f'(0)=1,f(x)!=0 for any x.Findf(x)

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1+x) then (1) g(x) is an odd function (2)g(x) is an even function (3) graph of f(x) is symmetrical about the line x=1 (4) f'(1)=0

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2) (0) = 1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R . then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AA x,y in R and f(0)!=0 ,then f(x) is an even function f(x) is an odd function If f(2)=a, then f(-2)=a If f(4)=b, then f(-4)=-b