What is the range of f(x)=ln(x)-ln(x+1) ?

The range of f(x)=ln(x)-ln(x+1) is f(x) 0

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range of f(x)=ln(x)-ln(x+1)

range

f (x) = ln (x) - ln (x + 1)

f (x) < 0 or f (x) > 0

Interval Notation

(- \infty, 0) \cup (0, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

ln (x) - ln (x + 1)

Inverse of

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

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

Find the domain of each inverse function

Domain of

- \frac{e ^{x}}{e ^{x} - 1} : x < 0 or x > 0

Combine the intervals

f (x) < 0 or f (x) > 0

x^{5} - x^{3}

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

f (x) = 20 - 2 x^{2}

f (x) = x^{4} - 6 x^{2}

f (x) = \frac{x ^{3}}{x ^{2} - 25}

What is the range of f(x)=ln(x)-ln(x+1) ?
The range of f(x)=ln(x)-ln(x+1) is f(x)<0\lor f(x)>0