What is the inverse of f(x)= 1/2 sqrt(x+4)-5 ?

The inverse of f(x)= 1/2 sqrt(x+4)-5 is 4x^2+40x+96

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inverse of f(x)= 1/2 sqrt(x+4)-5

inverse

f (x) = \frac{1}{2} x + 4 - 5

4 x^{2} + 40 x + 96

Solution steps

y = \frac{1}{2} x + 4 - 5

Replace

x

with

y

x = \frac{1}{2} y + 4 - 5

Solve for

y, x = \frac{1}{2} y + 4 - 5

4 x^{2} + 40 x + 96

(5.2) (7.8)

y = - x^{2} + 3

f (x) = \frac{x - 1}{25 - x ^{2}}

f (x) = 6 x - x^{2}, x \leq 3

G

What is the inverse of f(x)= 1/2 sqrt(x+4)-5 ?
The inverse of f(x)= 1/2 sqrt(x+4)-5 is 4x^2+40x+96