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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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

\frac{x ^{2} + 3 x - 10}{x ^{2} + 10 x + 25}

f (x) = 3 ln (x)

f (x) = x \frac{1}{4} - 3

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

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