What is the inverse of f(x)=(x-2)^4 ?

The inverse of f(x)=(x-2)^4 is \sqrt[4]{x}+2,-\sqrt[4]{x}+2

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inverse of f(x)=(x-2)^4

inverse

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

Solution steps

y = (x - 2)^{4}

Replace

x

with

y

x = (y - 2)^{4}

Solve for

y, x = (y - 2)^{4}

2 x^{2} - x + 2

f (x) = - x^{3} + 9 x^{2} - 53

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

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

f (x) = 3 \cdot 0. 2^{x}

What is the inverse of f(x)=(x-2)^4 ?
The inverse of f(x)=(x-2)^4 is \sqrt[4]{x}+2,-\sqrt[4]{x}+2