What is the range of (20)/(10+e^x) ?

The range of (20)/(10+e^x) is 0<f(x)<2

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range of (20)/(10+e^x)

range

\frac{20}{10 + e ^{x}}

0 < f (x) < 2

Interval Notation

(0, 2)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{20}{10 + e ^{x}}

Inverse of

\frac{20}{10 + e ^{x}} : ln (\frac{20}{x} - 10)

ln (\frac{20}{x} - 10)

Find the domain of each inverse function

Domain of

ln (\frac{20}{x} - 10) : 0 < x < 2

Combine the intervals

0 < f (x) < 2

f (x) = 4 x^{2} + 8 x + 3

f (x) = 5 x^{3} - 3

2 cos^{2} (x)

x - 18

f (x) = \frac{- 31 ( x - 1 ) ^{2}}{x - 5}