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Question
Select the correct answer from given alternatives.
Let the function f be defined by f(x) = `(2x + 1)/(1 - 3x)` then f–1 (x) is ______.
Options
`(x - 1)/(3x + 2)`
`(x + 1)/(3x - 2)`
`(2x + 1)/(1 - 3x)`
`(3x + 2)/(x - 1)`
Solution
Let the function f be defined by f(x) = `(2x + 1)/(1 - 3x)` then f–1 (x) is `underline((x - 1)/(3x + 2))`.
Explanation:
f(x) = `(2x + 1)/(1 - 3x)` = y say. Then
2x + 1 = y (1 – 3x)\
∴ y – 1 = x (2 + 3y)
∴ x = `("y" - 1)/(2 + 3"y")` = f-1 (y)
∴ f-1 (x) = `("x" - 1)/(2 + 3"x")`
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