What is the inverse of f(x)=sqrt(20.25-(x+2.5)^2)+2 ?

The inverse of f(x)=sqrt(20.25-(x+2.5)^2)+2 is -(5+sqrt(-4x^2+16x+65))/2 ,-(5-sqrt(-4x^2+16x+65))/2

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inverse of f(x)=sqrt(20.25-(x+2.5)^2)+2

inverse

f (x) = 20.25 - (x + 2.5)^{2} + 2

- \frac{5 + - 4 x ^{2} + 16 x + 65}{2}, - \frac{5 - - 4 x ^{2} + 16 x + 65}{2}

Solution steps

y = 20.25 - (x + 2.5)^{2} + 2

Replace

x

with

y

x = 20.25 - (y + 2.5)^{2} + 2

Solve for

y, x = 20.25 - (y + 2.5)^{2} + 2

- \frac{5 + - 4 x ^{2} + 16 x + 65}{2}, - \frac{5 - - 4 x ^{2} + 16 x + 65}{2}

(- 4, - 9), (- 8, 1)

ln (5 - 3 x^{2})

f (x) = 12 x

\frac{3 + 4 x}{1 - 5 x}

f (x) = \frac{( 5 x - 1 )}{( - 1 + 5 x )}

What is the inverse of f(x)=sqrt(20.25-(x+2.5)^2)+2 ?
The inverse of f(x)=sqrt(20.25-(x+2.5)^2)+2 is -(5+sqrt(-4x^2+16x+65))/2 ,-(5-sqrt(-4x^2+16x+65))/2