What is the inverse of f(x)=(sqrt(x)+4)/(3-sqrt(x)) ?

The inverse of f(x)=(sqrt(x)+4)/(3-sqrt(x)) is (16-24x+9x^2)/(1+2x+x^2)

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inverse of f(x)=(sqrt(x)+4)/(3-sqrt(x))

inverse

f (x) = \frac{x + 4}{3 - x}

\frac{16 - 24 x + 9 x ^{2}}{1 + 2 x + x ^{2}}

Solution steps

y = \frac{x + 4}{3 - x}

Replace

x

with

y

x = \frac{y + 4}{3 - y}

Solve for

y, x = \frac{y + 4}{3 - y}

\frac{16 - 24 x + 9 x ^{2}}{1 + 2 x + x ^{2}}

y = \frac{4}{- x - 2} + 2

\frac{3 x - 4}{2 x - 1}

8 x - 8

f (x) = \frac{3 x - 7}{5 x + 6}

\frac{( 2 x + 3 )}{x - 1}

What is the inverse of f(x)=(sqrt(x)+4)/(3-sqrt(x)) ?
The inverse of f(x)=(sqrt(x)+4)/(3-sqrt(x)) is (16-24x+9x^2)/(1+2x+x^2)