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

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

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

inverse

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

\frac{3 x + 1 - 2}{3}, \frac{- 3 x + 1 - 2}{3}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{3 x + 1 - 2}{3}, \frac{- 3 x + 1 - 2}{3}

y = - \frac{( x ^{2} + 27 )}{6}

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

12 - 2 x - \frac{3}{2}

f (x) = \frac{7 x + 15}{2}

f (x) = (1 + x)^{2} + 2 x^{2}

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