What is the inverse of f(x)=sqrt(4-25/9 (x+2)^2) ?

The inverse of f(x)=sqrt(4-25/9 (x+2)^2) is -(10+3sqrt(-x^2+4))/5 ,-(10-3sqrt(-x^2+4))/5

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inverse of f(x)=sqrt(4-25/9 (x+2)^2)

inverse

f (x) = 4 - \frac{25}{9} (x + 2)^{2}

- \frac{10 + 3 - x ^{2} + 4}{5}, - \frac{10 - 3 - x ^{2} + 4}{5}

Solution steps

y = 4 - \frac{25}{9} (x + 2)^{2}

Replace

x

with

y

x = 4 - \frac{25}{9} (y + 2)^{2}

Solve for

y, x = 4 - \frac{25}{9} (y + 2)^{2}

- \frac{10 + 3 - x ^{2} + 4}{5}, - \frac{10 - 3 - x ^{2} + 4}{5}

f (n) = \frac{- 16 + n}{4}

f (x) = x^{2} - 4 x - 12

f (x) = \frac{2 x + 3}{5 - x}

f (x) = \frac{1}{2} x^{2} + 9 x + 8

(- 1) (- 3)

What is the inverse of f(x)=sqrt(4-25/9 (x+2)^2) ?
The inverse of f(x)=sqrt(4-25/9 (x+2)^2) is -(10+3sqrt(-x^2+4))/5 ,-(10-3sqrt(-x^2+4))/5