What is the inverse of f(x)= 1/3 (x-2)^2+8 ?

The inverse of f(x)= 1/3 (x-2)^2+8 is sqrt(3x-24)+2,-sqrt(3x-24)+2

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inverse of f(x)= 1/3 (x-2)^2+8

inverse

f (x) = \frac{1}{3} (x - 2)^{2} + 8

3 x - 24 + 2, - 3 x - 24 + 2

Solution steps

y = \frac{1}{3} (x - 2)^{2} + 8

Replace

x

with

y

x = \frac{1}{3} (y - 2)^{2} + 8

Solve for

y, x = \frac{1}{3} (y - 2)^{2} + 8

3 x - 24 + 2, - 3 x - 24 + 2

2 ln (\frac{x + 3}{5})

y = x - 8

\frac{2 x}{x ^{2} - 1}

f (x) = ln (x + 3) + 5

What is the inverse of f(x)= 1/3 (x-2)^2+8 ?
The inverse of f(x)= 1/3 (x-2)^2+8 is sqrt(3x-24)+2,-sqrt(3x-24)+2