What is the inverse of f(x)= 4/3 x^2-4 ?

The inverse of f(x)= 4/3 x^2-4 is (sqrt(3x+12))/2 ,-(sqrt(3x+12))/2

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inverse of f(x)= 4/3 x^2-4

inverse

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

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

Solution steps

y = \frac{4}{3} x^{2} - 4

Replace

x

with

y

x = \frac{4}{3} y^{2} - 4

Solve for

y, x = \frac{4}{3} y^{2} - 4

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

f (x) = x^{2} - 4 x - 21

f (x) = x^{2} - 4 x - 10

5 x - 15

f (x) = 6 x^{3} + 3

f (x) = 6 x^{3} + 8

What is the inverse of f(x)= 4/3 x^2-4 ?
The inverse of f(x)= 4/3 x^2-4 is (sqrt(3x+12))/2 ,-(sqrt(3x+12))/2