Let g(x) be a polynomial of degree one and f(x) be defined by `f(x)=-{g(x), x<=0 and |x|^sinx, x>0` If f(x) is continuous satisfying `f'(1)=f(-1)`, then g(x) is

Let g(x) be a polynomial of degree one and f(x) be defined by f(x)=-g(x), x 0 If f(x) is continuous satisfying f'(1)=f(-1) , then g(x) is

Let g(x) be a polynomial of degree one and f(x) is defined by f(x)={g(x),x 0} Find g(x) such that f(x) is continuous and f'(1)=f(-1)

Let g(x) be a polynomial of degree one and f(x) is defined by f(x)={g(x) , xleq0 and ((1+x)/(2+x))^(1/x) , xgt0 } Find g(x) such that f(x) is continuous and f'(1)=f(-1)

Let f(x) be a polynomial of degree one and f(x) be a function defined by f(x)={(g(x), x le0), ((1+x)/(2+x)^(1//x), x gt0):} If f(x) is continuous at x=0 and f(-1)=f'(1), then g(x) is equal to :

Let f(x) be polynomial function of degree 2 such that f(x)gt0 for all x in R. If g(x)=f(x)+f'(x)+f''(x) for all x, then

Let f(x) be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x g(x)"For all "x,y in R , where g(x) is continuous. Then,

Let f(x) be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x g(x)"For all "x,y in R , where g(x) is continuous. Then,

Let f(x+y)=f(x)f(y) and f(x) = 1 + (sin2x) g(x) where g(x) is continuous . Then f^(1) (x) equals

Let [x] denote the integral part of x in R and g(x)=x-[x]. Let f(x) be any continuous function with f(0)=f(1) then the function h(x)=f(g(x)

Let [x] denote the integral part of x in R and g(x) = x- [x] . Let f(x) be any continuous function with f(0) = f(1) then the function h(x) = f(g(x) :