What is the inverse of f(x)=sqrt(((12-4x))/((12-x))) ?

The inverse of f(x)=sqrt(((12-4x))/((12-x))) is (12-12x^2)/(-x^2+4)

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inverse of f(x)=sqrt(((12-4x))/((12-x)))

inverse

f (x) = \frac{( 12 - 4 x )}{( 12 - x )}

\frac{12 - 12 x ^{2}}{- x ^{2} + 4}

Solution steps

y = \frac{12 - 4 x}{12 - x}

Replace

x

with

y

x = \frac{12 - 4 y}{12 - y}

Solve for

y, x = \frac{12 - 4 y}{12 - y}

\frac{12 - 12 x ^{2}}{- x ^{2} + 4}

What is the inverse of f(x)=sqrt(((12-4x))/((12-x))) ?
The inverse of f(x)=sqrt(((12-4x))/((12-x))) is (12-12x^2)/(-x^2+4)