What is the inverse of f(x)=4^{1/(x-2)} ?

The inverse of f(x)=4^{1/(x-2)} is (2ln(2))/(ln(x))+2

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

inverse

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

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

Solution steps

y = 4^{\frac{1}{x - 2}}

Replace

x

with

y

x = 4^{\frac{1}{y - 2}}

Solve for

y, x = 4^{\frac{1}{y - 2}}

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

f (x) = - \frac{1}{2} x + 3 + 4

f (x) = x^{(\frac{1}{3})}

f (x) = x^{2} - 4, x \geq 2

f (x) = 7.8019 - 0.7714 x + 0.0149 x^{2}

f (x) = 3 x + 3

What is the inverse of f(x)=4^{1/(x-2)} ?
The inverse of f(x)=4^{1/(x-2)} is (2ln(2))/(ln(x))+2