Let f : R → R be defined by f(x) = 3x − 4. The function f is: A. one-one but not onto B. onto but not one-one C. bijective D. neither one-one nor onto Answer: C) bijective Explanation: f(x₁) = f(x₂) → 3x₁ − 4 = 3x₂ − 4 → x₁ = x₂ → one-one. For any y ∈ R, x = (y+4)/3 ∈ R and f(x) = y → onto. Hence bijective.

imo class 12 relations and functions

Let f : R → R be defined by f(x) = 3x − 4. The function f is:

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Let f : R → R be defined by f(x) = 3x − 4. The function f is:

Answer: C) bijective

Explanation: f(x₁) = f(x₂) → 3x₁ − 4 = 3x₂ − 4 → x₁ = x₂ → one-one. For any y ∈ R, x = (y+4)/3 ∈ R and f(x) = y → onto. Hence bijective.