What is the range of f(x)=log_{2}((1+x)/(1-x)) ?

The range of f(x)=log_{2}((1+x)/(1-x)) is -infinity <f(x)<infinity

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range of f(x)=log_{2}((1+x)/(1-x))

range

f (x) = lo g_{2} (\frac{1 + x}{1 - x})

- \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:

lo g_{2} (\frac{1 + x}{1 - x})

Inverse of

lo g_{2} (\frac{1 + x}{1 - x}) : - \frac{1 - 2 ^{x}}{2 ^{x} + 1}

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

- \infty < f (x) < \infty

f (x) = \frac{x ^{2}}{x - 9}

f (x) = \frac{x ^{3} - 4 x}{3 x ^{2} + 3 x - 6}

f (x) = 100 - 3 x

e^{x + 1}

arcsin (x)

What is the range of f(x)=log_{2}((1+x)/(1-x)) ?
The range of f(x)=log_{2}((1+x)/(1-x)) is -infinity <f(x)<infinity