What is the range of f(x)=log_{2}(2^x) ?

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

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range of f(x)=log_{2}(2^x)

range

f (x) = lo g_{2} (2^{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} (2^{x})

Inverse of

lo g_{2} (2^{x}) : x

x

Find the domain of each inverse function

Domain of

x : - \infty < x < \infty

Combine the intervals

- \infty < f (x) < \infty

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