TS EAMCET · Maths · Functions
\(f:[-\infty, 0] \rightarrow[0, \infty)\) is defined as \(f(x)=x^2\). The domain and range of its inverse is
- A Domain \(\left(f^{-1}\right)=[0, \infty)\), Range of \(\left(f^{-1}\right\}=(-\infty, 0]\)
- B Domain of \(\left(f^{-1}\right\}=[0, \infty)\), Range of \(\left(f^{-1}\right)=(-\infty, \infty]\)
- C Dornain of \(\left(f^{-1}\right\}=[0, \infty)\), Range of \(\left(f^{-1}\right\}=(0, \infty)\)
- D \(f^{-1}\) does not exist
Answer & Solution
Correct Answer
(A) Domain \(\left(f^{-1}\right)=[0, \infty)\), Range of \(\left(f^{-1}\right\}=(-\infty, 0]\)
Step-by-step Solution
Detailed explanation
We have a function \(f:(-\infty, 0] \rightarrow[0, \infty)\) defined as \(f(x)=x^2\). The graph of above function is Since, each line parallel to \(x\) axis cuts the above curve at maximum one point, therefore \(f\) is one one. Also from the graph it is clear that range…
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