Relations and Functions
NCERT Class 12
CBSE
Grade 12
Question:
Show that the function $f: \mathbb{R} \rightarrow \mathbb{R}$ given by $f(x) = 2x$ is one-one and onto.
Step-by-Step Solution
One-one: $f(x_1) = f(x_2) \Rightarrow 2x_1 = 2x_2 \Rightarrow x_1 = x_2$. [1.0 Mark]
Onto: For any $y \in \mathbb{R}$, $x = y/2 \in \mathbb{R} \Rightarrow f(y/2) = y$. Proved! [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Proving One-one (Injective): 1.0 Mark
Proving Onto (Surjective): 1.0 Mark
Correct Answer:
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