What is the range of ln((x+1)/2) ?

The range of ln((x+1)/2) is -infinity <f(x)<infinity

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range of ln((x+1)/2)

range

ln (\frac{x + 1}{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 + 1}{2})

Inverse of

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

e^{x} \cdot 2 - 1

Find the domain of each inverse function

Domain of

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

Combine the intervals

- \infty < f (x) < \infty

\frac{x ^{3}}{3} - x^{2} - 15 x

25 - x^{2} - x + 3

f (x) = \frac{x + 1}{x + 7}

a^{x}

f (x) = (x - 1) e^{- x}

What is the range of ln((x+1)/2) ?
The range of ln((x+1)/2) is -infinity <f(x)<infinity