If `f(x)` is an even function and satisfies the relation `x^2dotf(x)-2f(1/x)=g(x),w h e r eg(x)` is an odd function, then find the value of `f(5)dot`

If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) for all x ,

A continuous function f(x) satisfies the relation f(x)=e^x+int_0^1 e^xf(t)dt then f(1)=

A Function f(x) satisfies the relation f(x)=e^x+int_0^1e^xf(t)dtdot Then (a) f(0) 0

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))dot

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))dot

Let G(x)=(1/(a^x-1)+1/2)F(x), where a is a positive real number not equal to 1 and f(x) is an odd function. Which of the following statements is true? (a) G(x) is an odd function (b) G(x)i s an even function (c) G(x) is neither even nor odd function. (d)Whether G(x) is an odd or even function depends on the value of a

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

If f(x) and g(x)=f(x)sqrt(1-2(f(x))^2) are strictly increasing AAx in R , then find the values of f(x)dot

If f(x) is a polynomial function satisfying f(x)dotf(1/x)=f(x)+f(1/x) and f(4)=65 ,t h e nfin df(6)dot

If f(x) is an odd function, f(1)=3,f(x+2)=f(x)+f(2), then the value of f(3) is________