What is the inverse of f(x)=sqrt(4-\sqrt{4-x)} ?

The inverse of f(x)=sqrt(4-\sqrt{4-x)} is -x^4+8x^2-12

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inverse of f(x)=sqrt(4-\sqrt{4-x)}

inverse

f (x) = 4 - 4 - x

- x^{4} + 8 x^{2} - 12

Solution steps

y = 4 - 4 - x

Replace

x

with

y

x = 4 - 4 - y

Solve for

y, x = 4 - 4 - y

- x^{4} + 8 x^{2} - 12

f (n) = \frac{- 9 + n}{3}

f (x) = - x^{2} + 6 x - 1

x = 3^{y}

f (x) = 2 + lo g_{2} (1 - x)

y = - 3 x + 12

What is the inverse of f(x)=sqrt(4-\sqrt{4-x)} ?
The inverse of f(x)=sqrt(4-\sqrt{4-x)} is -x^4+8x^2-12