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

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

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

inverse

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

\frac{3 + 4 x ^{2}}{3 x ^{2} - 2}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{3 + 4 x ^{2}}{3 x ^{2} - 2}

f (x) = \frac{5}{7} x + 4

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

y = - 3 x^{2} + 100 x + 1

f (x) = 19 x^{2} - 17

f (x) = 8 x - 2 + 5

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