What is the inverse of f(x)=(x^{1/3}+7)^7 ?

The inverse of f(x)=(x^{1/3}+7)^7 is x^{3/7}-21x^{2/7}+147\sqrt[7]{x}-343

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inverse of f(x)=(x^{1/3}+7)^7

inverse

f (x) = (x^{\frac{1}{3}} + 7)^{7}

Solution steps

y = (x^{\frac{1}{3}} + 7)^{7}

Replace

x

with

y

x = (y^{\frac{1}{3}} + 7)^{7}

Solve for

y, x = (y^{\frac{1}{3}} + 7)^{7}

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

f (x) = \frac{x}{16 - x}

f (x) = 9 - 8 x - 4 x^{2}

f (x) = - 16 x^{2} + 30 x + 3

What is the inverse of f(x)=(x^{1/3}+7)^7 ?
The inverse of f(x)=(x^{1/3}+7)^7 is x^{3/7}-21x^{2/7}+147\sqrt[7]{x}-343