IF `f(x)=1/(x+1)-log(1+x),xgt0` , then f is

If 3f(x)-f(1/x)=log_(e)x^(4)(xgt0) , then prove that f(e^(x))=x .

3f(x)-f(1/x)=log_(e)x^(4)(xgt0) , then f(10^(-x)) is equal to

If g(x)=ln(1+x)(tan^(-1)x)/(1+x),xgt0 then sgn(g(x)) is,(where sgn(.) represents signum function)

Given : f(x)=x^((1)/(x)),(xgt0) has the maximum value at x=e , then

Let f(x) be differntiable on the interval (0,oo) such that f(1)=1 and lim_(t tox)(t^(2)f(x)-x^(2)f(t))/(t-x)=1 for each xgt0 . Then f(x) is :

If f(x)=int_(1)^(x)(log_(e)t)/(1+t)dt , where xgt0 , find the value of f(x)+f((1)/(x)) and hence show that, f(e)+f((1)/(e))=(1)/(2) .

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)