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Question
Let `f : R {(-1)/3} → R - {0}` be defined as `f(x) = 5/(3x + 1)` is invertible. Find f–1(x).
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Solution
Given, `f(x) = 5/(3x + 1)` and is invertible.
So, we must check for invertibility.
Now, let f(x) = y = `5/(3x + 1)`
`\implies` y(3x + 1) = 5
`\implies` 3xy + y = 5
`\implies` 3xy = 5 – y
`\implies x = (5 - y)/(3y)`
∴ `f^-1(y) = (5 - y)/(3y)`
Now put y = x
`\implies f^-1(x) = (5 - x)/(3x)`
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