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

The inverse of (2x-3)/(sqrt(x)) is (12+x^2+xsqrt(x^2+24))/8 ,(12+x^2-xsqrt(x^2+24))/8

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inverse of (2x-3)/(sqrt(x))

inverse

\frac{2 x - 3}{x}

\frac{12 + x ^{2} + x x ^{2} + 24}{8}, \frac{12 + x ^{2} - x x ^{2} + 24}{8}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{12 + x ^{2} + x x ^{2} + 24}{8}, \frac{12 + x ^{2} - x x ^{2} + 24}{8}

x^{2} + 10 x

y = 3 x + 9

f (x) = 2^{x + 1}, x \leq - 1

\frac{x}{5} + 3

f (x) = (x + 1)^{2}, x \leq - 2

What is the inverse of (2x-3)/(sqrt(x)) ?
The inverse of (2x-3)/(sqrt(x)) is (12+x^2+xsqrt(x^2+24))/8 ,(12+x^2-xsqrt(x^2+24))/8