What is the inverse of f(x)=2^{1/x},x>0 ?

The inverse of f(x)=2^{1/x},x>0 is (ln(2))/(ln(x))

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inverse of f(x)=2^{1/x},x>0

inverse

f (x) = 2^{\frac{1}{x}}, x > 0

\frac{ln ( 2 )}{ln ( x )}

Solution steps

y = 2^{\frac{1}{x}}

Replace

x

with

y

x = 2^{\frac{1}{y}}

Solve for

y, x = 2^{\frac{1}{y}}

\frac{ln ( 2 )}{ln ( x )}

f (x) = 2 (x - 1)^{2} - 4

(x + 3)^{2} - 4

1.1

1.4

8 cos (π^{2} x - π^{4}) - 3

What is the inverse of f(x)=2^{1/x},x>0 ?
The inverse of f(x)=2^{1/x},x>0 is (ln(2))/(ln(x))