What is the range of f(x)= 4/(1+2(0.5)^x) ?

The range of f(x)= 4/(1+2(0.5)^x) is 0<f(x)<4

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range of f(x)= 4/(1+2(0.5)^x)

range

f (x) = \frac{4}{1 + 2 ( 0.5 ) ^{x}}

0 < f (x) < 4

Interval Notation

(0, 4)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{4}{1 + 20. 5 ^{x}}

Inverse of

\frac{4}{1 + 20. 5 ^{x}} : \frac{ln ( \frac{4 - x}{2 x} )}{ln ( 0.5 )}

\frac{ln ( \frac{4 - x}{2 x} )}{ln ( 0.5 )}

Find the domain of each inverse function

Domain of

\frac{ln ( \frac{4 - x}{2 x} )}{ln ( 0.5 )} : 0 < x < 4

Combine the intervals

0 < f (x) < 4

3 x^{2} - x - 5

f (x) = 3 x^{2} - 6

2 x + y = - 4

3 x - 2 y = - 24

What is the range of f(x)= 4/(1+2(0.5)^x) ?
The range of f(x)= 4/(1+2(0.5)^x) is 0<f(x)<4