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

The inverse of f(x)=(2sqrt(x+6))/3 is (9x^2)/4-6

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inverse of f(x)=(2sqrt(x+6))/3

inverse

f (x) = \frac{2 x + 6}{3}

\frac{9 x ^{2}}{4} - 6

Solution steps

y = \frac{2 x + 6}{3}

Replace

x

with

y

x = \frac{2 y + 6}{3}

Solve for

y, x = \frac{2 y + 6}{3}

\frac{9 x ^{2}}{4} - 6

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

7 x + 3

x^{2} + 5 x + 6

f (x) = - - x

lo g_{5} (x)

What is the inverse of f(x)=(2sqrt(x+6))/3 ?
The inverse of f(x)=(2sqrt(x+6))/3 is (9x^2)/4-6