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If f(x) = , then f-1(x) = ?

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Detailed Solution

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Concept:

Functions:

If y = f(x), then we say that x = f-1(y).

Calculation:

Let y = f(x) = .

⇒ y(1 + x) = 1 - x

⇒ y + xy = 1 - x

⇒ xy + x = 1 - y

⇒ x(1 + y) = 1 - y

⇒ x =  = f-1(y)

Replacing y by x, we can say that:

f-1(x) = .

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