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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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