What is the range of #y = 2^x-1#?

1 Answer
bp
May 30, 2015

The range of the given function can be determined by comparing this with the graph of #y=2^x# . Its range is (0,#oo#).

The given function is a vertical shift down by 1. Hence its range would be (-1,#oo#)

Alternatively, interchange x and y and find the domain of the new function. Accordingly, x=#2^y#-1, that is #2^y#= x+1. Now take natural log on both sides, y=#1/ln2 ln(x+1)#

The domain of this function is all real values of x greater than -1, that is (-1,#oo#)

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