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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