What is the inverse of f(x)=(\sqrt[4]{x}+4)^7 ?

The inverse of f(x)=(\sqrt[4]{x}+4)^7 is x^{4/7}-16x^{3/7}+96x^{2/7}-256\sqrt[7]{x}+256

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inverse of f(x)=(\sqrt[4]{x}+4)^7

inverse

x^{\frac{4}{7}} - 16 x^{\frac{3}{7}} + 96 x^{\frac{2}{7}} - 256 7 x + 256

Solution steps

y = (4 x + 4)^{7}

Replace

x

with

y

x = (4 y + 4)^{7}

Solve for

y, x = (4 y + 4)^{7}

x^{\frac{4}{7}} - 16 x^{\frac{3}{7}} + 96 x^{\frac{2}{7}} - 256 7 x + 256

What is the inverse of f(x)=(\sqrt[4]{x}+4)^7 ?
The inverse of f(x)=(\sqrt[4]{x}+4)^7 is x^{4/7}-16x^{3/7}+96x^{2/7}-256\sqrt[7]{x}+256