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Relations and Functions
NCERT Class 12
CBSE
Grade 12
Question:
Let $A = \mathbb{R} - \{3\}$ and $B = \mathbb{R} - \{1\}$. Consider the function $f: A \rightarrow B$ defined by $f(x) = \dfrac{x - 2}{x - 3}$. Is $f$ one-one and onto? Justify your answer.
Step-by-Step Solution
One-one: $(x_1-2)(x_2-3) = (x_2-2)(x_1-3) \Rightarrow x_1 = x_2$. [1.5 Marks] Onto: $x = \dfrac{3y-2}{y-1} \in A$ for all $y \in B \Rightarrow f$ is onto. [1.5 Marks]
--- 🎯 Official CBSE Marking Scheme: Proving One-one: 1.5 Marks Proving Onto: 1.5 Marks
Correct Answer:
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