What is the inverse of f(x)=(x-1)^4-1 ?

The inverse of f(x)=(x-1)^4-1 is \sqrt[4]{x+1}+1,-\sqrt[4]{x+1}+1

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inverse of f(x)=(x-1)^4-1

inverse

f (x) = (x - 1)^{4} - 1

Solution steps

y = (x - 1)^{4} - 1

Replace

x

with

y

x = (y - 1)^{4} - 1

Solve for

y, x = (y - 1)^{4} - 1

f (x) = y - 5 = \frac{1}{2} (x + 16)^{2}

f (x) = 5 (x + 10)^{\frac{1}{3}} - 8

f (x) = \frac{( - 2 x - 5 )}{- 8 x + 5}

y = 2 x^{2} - 5 x

5 x^{2} + 5 x

What is the inverse of f(x)=(x-1)^4-1 ?
The inverse of f(x)=(x-1)^4-1 is \sqrt[4]{x+1}+1,-\sqrt[4]{x+1}+1