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

The inverse of f(x)=(x(3x-1))/2 is (1+sqrt(1+24x))/6 ,(1-sqrt(1+24x))/6

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

inverse

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

\frac{1 + 1 + 24 x}{6}, \frac{1 - 1 + 24 x}{6}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{1 + 1 + 24 x}{6}, \frac{1 - 1 + 24 x}{6}

5 x - 2

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

3 - 3 - x

f (x) = (x + 9)^{5}

f (x) = ln (sin (\frac{3 π}{4}) - 1)

What is the inverse of f(x)=(x(3x-1))/2 ?
The inverse of f(x)=(x(3x-1))/2 is (1+sqrt(1+24x))/6 ,(1-sqrt(1+24x))/6