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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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

+ 2 tan (x - \frac{π}{4})

(8 - 2 x)^{2}

2 + x - 6

f (x) = (3 x - 2)^{3}

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