What is the answer to solvefor f,f^{-1}(x)=x^2+1 ?

The answer to solvefor f,f^{-1}(x)=x^2+1 is f= x/(x^2+1);\quad x\ne i,x\ne-i

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solvefor f,f^{-1}(x)=x^2+1

solve for

f, f^{- 1} (x) = x^{2} + 1

f = \frac{x}{x ^{2} + 1}; x \neq = i, x \neq = - i

Solution steps

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

Refine

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

Multiply both sides by

f

x = x^{2} f + f

Switch sides

x^{2} f + f = x

Factor

x^{2} f + f : f (x^{2} + 1)

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

Divide both sides by

x^{2} + 1; x \neq = i, x \neq = - i

f = \frac{x}{x ^{2} + 1}; x \neq = i, x \neq = - i

4 n^{2} + 7 n + 1 = 0

x^{2} + 20 x + 51 = 0

x^{2} - x = 4 x

3 x^{2} - 8 x + 1 = - 2

2 x^{2} - 3 x - 36 = 0

What is the answer to solvefor f,f^{-1}(x)=x^2+1 ?
The answer to solvefor f,f^{-1}(x)=x^2+1 is f= x/(x^2+1);\quad x\ne i,x\ne-i