What is the inverse of f(x)=2+sqrt(1+\sqrt{x-1)} ?

The inverse of f(x)=2+sqrt(1+\sqrt{x-1)} is x^4-8x^3+22x^2-24x+10

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inverse of f(x)=2+sqrt(1+\sqrt{x-1)}

inverse

f (x) = 2 + 1 + x - 1

x^{4} - 8 x^{3} + 22 x^{2} - 24 x + 10

Solution steps

y = 2 + 1 + x - 1

Replace

x

with

y

x = 2 + 1 + y - 1

Solve for

y, x = 2 + 1 + y - 1

x^{4} - 8 x^{3} + 22 x^{2} - 24 x + 10

y = x - 8

\frac{y ^{2} + 1}{y ^{2} - 2 y}

6 x + 5 y = 30

y = x^{4} + 2

y = x + 3

What is the inverse of f(x)=2+sqrt(1+\sqrt{x-1)} ?
The inverse of f(x)=2+sqrt(1+\sqrt{x-1)} is x^4-8x^3+22x^2-24x+10