What is the inverse of f(x)=sqrt(10x-x^2) ?

The inverse of f(x)=sqrt(10x-x^2) is 5-sqrt(-x^2+25),sqrt(-x^2+25)+5

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inverse of f(x)=sqrt(10x-x^2)

inverse

f (x) = 10 x - x^{2}

5 - - x^{2} + 25, - x^{2} + 25 + 5

Solution steps

y = 10 x - x^{2}

Replace

x

with

y

x = 10 y - y^{2}

Solve for

y, x = 10 y - y^{2}

5 - - x^{2} + 25, - x^{2} + 25 + 5

f (x) = x - 0.005 x^{2}

f (x) = 0.5 x - 3

f (x) = - 2 (3 x + 1) + 4

4 - x

f (x) = 0.5 x + 6

What is the inverse of f(x)=sqrt(10x-x^2) ?
The inverse of f(x)=sqrt(10x-x^2) is 5-sqrt(-x^2+25),sqrt(-x^2+25)+5