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

The inverse of f(x)=(x(x-3))/(x-4) is (3+x+sqrt(x^2-10x+9))/2 ,(3+x-sqrt(x^2-10x+9))/2

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

inverse

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

\frac{3 + x + x ^{2} - 10 x + 9}{2}, \frac{3 + x - x ^{2} - 10 x + 9}{2}

Solution steps

y = \frac{x ( x - 3 )}{x - 4}

Replace

x

with

y

x = \frac{y ( y - 3 )}{y - 4}

Solve for

y, x = \frac{y ( y - 3 )}{y - 4}

\frac{3 + x + x ^{2} - 10 x + 9}{2}, \frac{3 + x - x ^{2} - 10 x + 9}{2}

What is the inverse of f(x)=(x(x-3))/(x-4) ?
The inverse of f(x)=(x(x-3))/(x-4) is (3+x+sqrt(x^2-10x+9))/2 ,(3+x-sqrt(x^2-10x+9))/2