What is the inverse of f(x)=2(x+4)^{1/5}-6 ?

The inverse of f(x)=2(x+4)^{1/5}-6 is (x^5}{32}+(45x^3)/4+(15x^4)/(16)+\frac{135x^2+405x)/2+239

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inverse of f(x)=2(x+4)^{1/5}-6

inverse

f (x) = 2 (x + 4)^{\frac{1}{5}} - 6

\frac{x ^{5}}{32} + \frac{45 x ^{3}}{4} + \frac{15 x ^{4}}{16} + \frac{135 x ^{2} + 405 x}{2} + 239

Solution steps

y = 2 (x + 4)^{\frac{1}{5}} - 6

Replace

x

with

y

x = 2 (y + 4)^{\frac{1}{5}} - 6

Solve for

y, x = 2 (y + 4)^{\frac{1}{5}} - 6

\frac{x ^{5}}{32} + \frac{45 x ^{3}}{4} + \frac{15 x ^{4}}{16} + \frac{135 x ^{2} + 405 x}{2} + 239

f (x) = (3 y + 2) (y + 1) 2

f (x) = 2 (3^{x + 1})

\frac{3}{2 x - 1}

g (x) = 2^{- x}

\frac{x}{x - 9}

What is the inverse of f(x)=2(x+4)^{1/5}-6 ?
The inverse of f(x)=2(x+4)^{1/5}-6 is (x^5}{32}+(45x^3)/4+(15x^4)/(16)+\frac{135x^2+405x)/2+239