What is the range of e^{1/x} ?

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range of e^{1/x}

range

e^{\frac{1}{x}}

0 < f (x) < 1 or f (x) > 1

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

e^{\frac{1}{x}}

Inverse of

e^{\frac{1}{x}} : \frac{1}{ln ( x )}

\frac{1}{ln ( x )}

Find the domain of each inverse function

Domain of

\frac{1}{ln ( x )} : 0 < x < 1 or x > 1

Combine the intervals

0 < f (x) < 1 or f (x) > 1

f (x) = 1 - 2 x^{2}

y = sec (x)

y = \frac{1}{2} x - 3

x^{2} + 8 x + 14

f (x) = \frac{( x + 2 ) ( x - 3 )}{2 x ^{2}}