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

The inverse of f(x)= 3/2 x^2+3 is sqrt((2x-6)/3),-sqrt((2x-6)/3)

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

inverse

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

\frac{2 x - 6}{3}, - \frac{2 x - 6}{3}

Solution steps

y = \frac{3}{2} x^{2} + 3

Replace

x

with

y

x = \frac{3}{2} y^{2} + 3

Solve for

y, x = \frac{3}{2} y^{2} + 3

\frac{2 x - 6}{3}, - \frac{2 x - 6}{3}

\frac{3 x - 7}{x + 3}

y = \frac{- 9 x + 7}{1 + x}

y = - 1.4 (x - 3.2)^{2} + 9.16

- \frac{2}{3} (x - 4)^{3}

f (x) = \frac{7 x}{( x - 4 )}

What is the inverse of f(x)= 3/2 x^2+3 ?
The inverse of f(x)= 3/2 x^2+3 is sqrt((2x-6)/3),-sqrt((2x-6)/3)