What is the range of ln((-x+2)/(x+2)) ?

The range of ln((-x+2)/(x+2)) is -infinity <f(x)<infinity

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range of ln((-x+2)/(x+2))

range

ln (\frac{- x + 2}{x + 2})

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

ln (\frac{- x + 2}{x + 2})

Inverse of

ln (\frac{- x + 2}{x + 2}) : \frac{2 - 2 e ^{x}}{e ^{x} + 1}

\frac{2 - 2 e ^{x}}{e ^{x} + 1}

Find the domain of each inverse function

Domain of

\frac{2 - 2 e ^{x}}{e ^{x} + 1} : - \infty < x < \infty

Combine the intervals

- \infty < f (x) < \infty

f (x) = 24 x - 2 x^{2}

f (x) = 2 x^{2} + x - 15

4 - 3 sin (\frac{2}{5} (x + 1))

f (x) = - 4

x^{2} + 1

What is the range of ln((-x+2)/(x+2)) ?
The range of ln((-x+2)/(x+2)) is -infinity <f(x)<infinity