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

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

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

solve for

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

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

Solution steps

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

Refine

\frac{x}{f} = x^{2} - 2

Multiply both sides by

f

x = x^{2} f - 2 f

Switch sides

x^{2} f - 2 f = x

Factor

x^{2} f - 2 f : f (x^{2} - 2)

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

Divide both sides by

x^{2} - 2; x \neq = 2, x \neq = - 2

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

f, f^{- 1} (x) = x^{2} - 4

d^{2} = 4 (3 d + 7)

- 2 x^{2} - 12 x - 8 = 0

(3 x - 7)^{2} + 4 = 29

s^{2} - 2 s - 14 = 0

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