TS EAMCET · Maths · Functions
Let \(x=\left\{\left[\begin{array}{ll}a & b \ c & d\end{array}\right]: a, b, c, d \in \mathbb{R}\right\}\). If \(f: X \rightarrow \mathbb{R}\) is defined by \(\mathrm{f}(\mathrm{A})=\operatorname{det}(\mathrm{A}) \forall \mathrm{A} \in \mathrm{X}\), then \(\mathrm{f}\) is
- A one-one but not onto
- B onto but not one-one
- C one-one and onto
- D neither one-one nor onto
Answer & Solution
Correct Answer
(B) onto but not one-one
Step-by-step Solution
Detailed explanation
\(x=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]=\mathrm{A}\) \(\operatorname{det} \mathrm{A}=\mathrm{f}(\mathrm{A})=a d-b c\) Let \(a=1, d=1, b=0, c=1\) \[ f(A)=1 \] Also if \(a=2, d=1, b=1, c=1\) \[ f(A)=1 \] \(\therefore f\) is not one-one but we know that…
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