What is the inverse of f(x)= 2/((x-1)^2)+3 ?

The inverse of f(x)= 2/((x-1)^2)+3 is sqrt(2/(x-3))+1,-sqrt(2/(x-3))+1

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inverse of f(x)= 2/((x-1)^2)+3

inverse

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

\frac{2}{x - 3} + 1, - \frac{2}{x - 3} + 1

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = \frac{2}{( y - 1 ) ^{2}} + 3

\frac{2}{x - 3} + 1, - \frac{2}{x - 3} + 1

y = \frac{3 x - 2}{x + 1}

f (x) = 5 + 4 x - 5

x^{2} - 12 x

f (x) = \frac{( x + 3 )}{8}

\frac{3 x ^{1 + \frac{1}{2}}}{8}

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