What is the inverse of f(x)=sqrt((2-x)/(x+5)) ?

The inverse of f(x)=sqrt((2-x)/(x+5)) is (2-5x^2)/(x^2+1)

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inverse of f(x)=sqrt((2-x)/(x+5))

inverse

f (x) = \frac{2 - x}{x + 5}

\frac{2 - 5 x ^{2}}{x ^{2} + 1}

Solution steps

y = \frac{2 - x}{x + 5}

Replace

x

with

y

x = \frac{2 - y}{y + 5}

Solve for

y, x = \frac{2 - y}{y + 5}

\frac{2 - 5 x ^{2}}{x ^{2} + 1}

What is the inverse of f(x)=sqrt((2-x)/(x+5)) ?
The inverse of f(x)=sqrt((2-x)/(x+5)) is (2-5x^2)/(x^2+1)