What is the range of f(x)=(12-e^x)/(6+e^x) ?

The range of f(x)=(12-e^x)/(6+e^x) is -1<f(x)<2

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range of f(x)=(12-e^x)/(6+e^x)

range

f (x) = \frac{12 - e ^{x}}{6 + e ^{x}}

- 1 < f (x) < 2

Interval Notation

(- 1, 2)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{12 - e ^{x}}{6 + e ^{x}}

Inverse of

\frac{12 - e ^{x}}{6 + e ^{x}} : ln (\frac{12 - 6 x}{x + 1})

ln (\frac{12 - 6 x}{x + 1})

Find the domain of each inverse function

Domain of

ln (\frac{12 - 6 x}{x + 1}) : - 1 < x < 2

Combine the intervals

- 1 < f (x) < 2

f (x) = \frac{3}{2 x + 5}

y = - \frac{5}{2} x - 5

2 x + 3 + 1

y = - \frac{1}{2} x - 2

5 sin (x)

What is the range of f(x)=(12-e^x)/(6+e^x) ?
The range of f(x)=(12-e^x)/(6+e^x) is -1<f(x)<2