MCQ
The function $f:R \to R$ defined by $f(x) = (x - 1)$ $(x - 2)(x - 3)$ is
- AOne-one but not onto
- ✓Onto but not one-one
- CBoth one-one and onto
- DNeither one-one nor onto
$f(1) = f(2) = f(3) = 0$ ==> $f(x)$ is not one-one.
For each $y \in R$, there exists $x \in R$ such that $f(x) = y$.
Therefore $f$ is onto. Hence $f:R \to R$ is onto but not one-one.
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$f(x) = \sqrt {\left| {{{\sin }^{ - 1}}\left| {\sin x} \right|} \right| - {{\cos }^{ - 1}}\left| {\cos x} \right|} $ is