What is the range of 3^{1/x} ?

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range of 3^{1/x}

range

3^{\frac{1}{x}}

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

Interval Notation

(0, 1) \cup (1, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

3^{\frac{1}{x}}

Inverse of

3^{\frac{1}{x}} : \frac{ln ( 3 )}{ln ( x )}

\frac{ln ( 3 )}{ln ( x )}

Find the domain of each inverse function

Domain of

\frac{ln ( 3 )}{ln ( x )} : 0 < x < 1 or x > 1

Combine the intervals

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

f (x) = tan (x + (\frac{7 π}{6}))

f (x) = x^{2} - 9 x + 3

f (x) = \frac{4}{x ^{2} + 1}

f (x) = ln ∣ 2 x - 3 ∣

49 - x^{2}