What is the inverse of f(x)=(sqrt(x)+6)/(5-sqrt(x)) ?

The inverse of f(x)=(sqrt(x)+6)/(5-sqrt(x)) is (36-60x+25x^2)/(1+2x+x^2)

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inverse of f(x)=(sqrt(x)+6)/(5-sqrt(x))

inverse

f (x) = \frac{x + 6}{5 - x}

\frac{36 - 60 x + 25 x ^{2}}{1 + 2 x + x ^{2}}

Solution steps

y = \frac{x + 6}{5 - x}

Replace

x

with

y

x = \frac{y + 6}{5 - y}

Solve for

y, x = \frac{y + 6}{5 - y}

\frac{36 - 60 x + 25 x ^{2}}{1 + 2 x + x ^{2}}

f (x) = \frac{3}{x} - 7

f (x) = \frac{12}{7 - 6 x}

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

f (x) = \frac{( x + 4 )}{x + 5}

\frac{1}{4} \cdot 1 0^{x - 3} + 5

What is the inverse of f(x)=(sqrt(x)+6)/(5-sqrt(x)) ?
The inverse of f(x)=(sqrt(x)+6)/(5-sqrt(x)) is (36-60x+25x^2)/(1+2x+x^2)