Let f : (0,1) → R be a function defined by

Question

Let f : (0,1) → \(\mathbb{R}\) be a function defined by

\(f(x)=\frac{1}{1-e^{-x}},\) and

g(x) = (f (-x) - f (x)) . Consider two statements 

(I) g is an increasing function in (0, 1) 

(II) g is one-one in (0, 1) Then, 

(1) Only (I) is true 

(2) Only (II) is true 

(3) Neither (I) nor (II) is true 

(4) Both (I) and (II) are true

Answer 1

(4) Both (I) and (II) are true