What is the inverse of f(x)=(2x+3)/(sqrt(4x-1)) ?

The inverse of f(x)=(2x+3)/(sqrt(4x-1)) is (-3+x^2+xsqrt(x^2-7))/2 ,(-3+x^2-xsqrt(x^2-7))/2

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inverse of f(x)=(2x+3)/(sqrt(4x-1))

inverse

f (x) = \frac{2 x + 3}{4 x - 1}

\frac{- 3 + x ^{2} + x x ^{2} - 7}{2}, \frac{- 3 + x ^{2} - x x ^{2} - 7}{2}

Solution steps

y = \frac{2 x + 3}{4 x - 1}

Replace

x

with

y

x = \frac{2 y + 3}{4 y - 1}

Solve for

y, x = \frac{2 y + 3}{4 y - 1}

\frac{- 3 + x ^{2} + x x ^{2} - 7}{2}, \frac{- 3 + x ^{2} - x x ^{2} - 7}{2}

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

3 x - 5

3 x - 6

g (x) = (x + 3)^{2} - 1

f (x) = 5 x^{2} - 5

What is the inverse of f(x)=(2x+3)/(sqrt(4x-1)) ?
The inverse of f(x)=(2x+3)/(sqrt(4x-1)) is (-3+x^2+xsqrt(x^2-7))/2 ,(-3+x^2-xsqrt(x^2-7))/2