What is the inverse of f(x)=((3^{x-3})/2)^{1/3} ?

The inverse of f(x)=((3^{x-3})/2)^{1/3} is (ln(2x^3))/(ln(3))+3

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inverse of f(x)=((3^{x-3})/2)^{1/3}

inverse

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

\frac{ln ( 2 x ^{3} )}{ln ( 3 )} + 3

Solution steps

y = (\frac{3 ^{x - 3}}{2})^{\frac{1}{3}}

Replace

x

with

y

x = (\frac{3 ^{y - 3}}{2})^{\frac{1}{3}}

Solve for

y, x = (\frac{3 ^{y - 3}}{2})^{\frac{1}{3}}

\frac{ln ( 2 x ^{3} )}{ln ( 3 )} + 3

What is the inverse of f(x)=((3^{x-3})/2)^{1/3} ?
The inverse of f(x)=((3^{x-3})/2)^{1/3} is (ln(2x^3))/(ln(3))+3