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Question
Answer the following:
Find whether the following function is one-one
f : R − {3} → R defined by f(x) = `(5x + 7)/(x - 3)` for x ∈ R − {3}
Solution
f : R − {3} → R defined by f(x) = `(5x + 7)/(x - 3)`
Let f(a) = f(b)
∴ `(5"a" + 7)/("a" - 3) = (5"b" + 7)/("b" - 3)`
∴ (5a + 7)(b – 3) = (a – 3)(5b + 7)
∴ 5ab – 15a + 7b – 21 = 5ab + 7a – 15b – 21
∴ – 22a = – 22b
∴ a = b
∴ f(a) = f(b) ⇒ a = b
∴ f is one-one.
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