What is the range of $y = 2^{x} - 1$ $y = 2^x-1$ ?

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What is the range of $y = 2^{x} - 1$ $y = 2^x-1$ ?

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Answer 1 · 2015-05-30T12:35:32

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

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

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

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

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What is the range of $y = 2^{x} - 1$ $y = 2^x-1$ ?

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