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

The inverse of f(x)=(2x)/(sqrt(3x-1)) is (3x^2+xsqrt(9x^2-16))/8 ,(3x^2-xsqrt(9x^2-16))/8

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

inverse

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

\frac{3 x ^{2} + x 9 x ^{2} - 16}{8}, \frac{3 x ^{2} - x 9 x ^{2} - 16}{8}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{3 x ^{2} + x 9 x ^{2} - 16}{8}, \frac{3 x ^{2} - x 9 x ^{2} - 16}{8}

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

\frac{( 3 x + 5 )}{x - 4}

f (x) = 16 x - 24

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

f (x) = \frac{9}{x - 9}

What is the inverse of f(x)=(2x)/(sqrt(3x-1)) ?
The inverse of f(x)=(2x)/(sqrt(3x-1)) is (3x^2+xsqrt(9x^2-16))/8 ,(3x^2-xsqrt(9x^2-16))/8