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}

Answer 1

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.