If `f(x)=(log)_e((x^2+e)/(x^2+1))` , then the range of `f(x)`

If f(x)=sin(log)_e{(sqrt(4-x^2))/(1-x)} , then the domain of f(x) is _____ and its range is __________.

Draw and graph of f(x) = (4log_(e)x)/(x^(2)) . Also find the range.

If f(x)=log_(e)((1-x)/(1+x)),|x| lt 1, " then " f((2x)/(1+x^(2))) is equal to

If f:[0,oo[vecR is the function defined by f(x)=(e^x^2-e^-x^2)/(e^x^2+e^-x^2), then check whether f(x) is injective or not.

Let f:R rarr R, f(x)=x+log_(e)(1+x^(2)) . Then

"If " f(x)=int(dx)/(x^(1//3)+2) " and "f(0)=12log_(e)2, " then the value of " f(-1) " is"-.

If f(x)=log[(1+x)/(1-x)], then prove that f[(2x)/(1+x^2)]=2f(x)dot

If d is the minimum distance between the curves f(x)=e^x a n dg(x)=(log)_e x , then the value of d^6 is

If f(x)=log_(e)(log_(e)x)/log_(e)x then f'(x) at x = e is

The range of f(x) = x^2 + 1 is