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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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

f (x) = - (x - 5) - 2

f (x) = 3 4 - x

(x + 4)^{2} - 1

f (x) = 3 4 x + 6

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