Identify-domain-and-range-of-this-function-that-f-x-ln-4-x-4-x-

Question Number 69974 by Shamim last updated on 29/Sep/19

Identify domain and range of this

function that f (x) = \ln \frac{4 - x}{4 + x} .

Commented by kaivan.ahmadi last updated on 29/Sep/19

\frac{4 - x}{4 + x} > 0 \Rightarrow - 4 < x < 4

\Rightarrow D_{f} = (- 4, 4)

y = l n \frac{4 - x}{4 + x} \Rightarrow e^{y} = \frac{4 - x}{4 + x} \Rightarrow 4 - x = 4 e^{y} + {x e}^{y} \Rightarrow

4 - 4 e^{y} = x + {x e}^{y} = x (1 + e^{y}) \Rightarrow x = \frac{4 - 4 e^{y}}{1 + e^{y}} \Rightarrow

f^{- 1} (x) = \frac{4 - 4 e^{x}}{1 + e^{x}}

R_{f} = D_{f^{- 1}} = R

Commented by Shamim last updated on 30/Sep/19

plz explain with details -

\frac{4 - x}{4 + x} > 0 \Rightarrow - 4 < x < 4

Commented by kaivan.ahmadi last updated on 30/Sep/19