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Question
Let f: R – `{3/5}` → R be defined by f(x) = `(3x + 2)/(5x - 3)`. Then ______.
Options
f–1(x) = f(x)
f–1(x) = – f(x)
(f o f)x = – x
f–1(x) = `1/19` f(x)
Solution
Let f: R – `{3/5}` → R be defined by f(x) = `(3x + 2)/(5x - 3)`. Then f–1(x) = f(x).
Explanation:
We have f(x) = `(3x + 2)/(5x - 3)` = y ......(Let)
⇒ 3x + 2 = 5xy – 3y
⇒ x(3 – 5y) = –3y – 2
⇒ x = `(3y + 2)/(5y - 3)`
⇒ f–1(x) = `(3x + 2)/(5x - 3)`
∴ f–1(x) = f(x)
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