What is the inverse of f(x)=sqrt(x(8-x)) ?

The inverse of f(x)=sqrt(x(8-x)) is 4-sqrt(-x^2+16),sqrt(-x^2+16)+4

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inverse of f(x)=sqrt(x(8-x))

inverse

f (x) = x (8 - x)

4 - - x^{2} + 16, - x^{2} + 16 + 4

Solution steps

y = x (8 - x)

Replace

x

with

y

x = y (8 - y)

Solve for

y, x = y (8 - y)

4 - - x^{2} + 16, - x^{2} + 16 + 4

f (x) = x^{2} + 7

\frac{x - 7}{x - 4}

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

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

f (x) = \frac{7 x}{6 x - 7}

What is the inverse of f(x)=sqrt(x(8-x)) ?
The inverse of f(x)=sqrt(x(8-x)) is 4-sqrt(-x^2+16),sqrt(-x^2+16)+4