AP EAMCET · Maths · Functions
If \(\mathrm{f}(\mathrm{x})\) and \(\mathrm{g}(\mathrm{x})\) are two real valued functions such that \(\mathrm{f}(\mathrm{g}(\mathrm{x}+\mathrm{y}))=\mathrm{f}(\mathrm{g}(\mathrm{x}))+\mathrm{f}(\mathrm{g}(\mathrm{y})), \mathrm{g}(1)=2\) and \(\mathrm{f}(2)=1\), then the function \(g(f(x))\) is discontinuous on the set
- A \(\mathbb{R}\)
- B \((0, \infty)\)
- C \((-\infty, 0)\)
- D \(\phi\)
Answer & Solution
Correct Answer
(A) \(\mathbb{R}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{f}(\mathrm{g}(\mathrm{x}+\mathrm{y}))=\mathrm{f}(\mathrm{g}(\mathrm{x}))+\mathrm{f}(\mathrm{g}(\mathrm{y}))\) ...(i) and \(f(2)=1, g(1)=2\) Now, from equation (i) :…
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