What is the inverse of y=((e^x+9)/2)^{1/3} ?

The inverse of y=((e^x+9)/2)^{1/3} is ln(2x^3-9)

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inverse of y=((e^x+9)/2)^{1/3}

inverse

y = (\frac{e ^{x} + 9}{2})^{\frac{1}{3}}

ln (2 x^{3} - 9)

Solution steps

y = (\frac{e ^{x} + 9}{2})^{\frac{1}{3}}

Replace

x

with

y

x = (\frac{e ^{y} + 9}{2})^{\frac{1}{3}}

Solve for

y, x = (\frac{e ^{y} + 9}{2})^{\frac{1}{3}}

ln (2 x^{3} - 9)

What is the inverse of y=((e^x+9)/2)^{1/3} ?
The inverse of y=((e^x+9)/2)^{1/3} is ln(2x^3-9)