What is the inverse of f(x)=2(-2x-5)^2-4,x>=-5/2 ?

The inverse of f(x)=2(-2x-5)^2-4,x>=-5/2 is -(sqrt((x+4)/2)+5)/(2),-(-sqrt((x+4)/2)+5)/(2)

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inverse of f(x)=2(-2x-5)^2-4,x>=-5/2

inverse

f (x) = 2 (- 2 x - 5)^{2} - 4, x \geq - \frac{5}{2}

- \frac{\frac{x + 4}{2} + 5}{2}, - \frac{- \frac{x + 4}{2} + 5}{2}

Solution steps

y = 2 (- 2 x - 5)^{2} - 4

Replace

x

with

y

x = 2 (- 2 y - 5)^{2} - 4

Solve for

y, x = 2 (- 2 y - 5)^{2} - 4

- \frac{\frac{x + 4}{2} + 5}{2}, - \frac{- \frac{x + 4}{2} + 5}{2}

y = (1 + x) (5 - x)

6000 (1 - \frac{25}{( x + 5 ) ^{2}})

f (x) = sin (o)

f (x) = (x + 8)^{2}, x \geq - 8

f (x) = \frac{( 6 - 6 x )}{( 3 - 7 x )}

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