ExamBro
ExamBro
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

  1. A \(\mathbb{R}\)
  2. B \((0, \infty)\)
  3. C \((-\infty, 0)\)
  4. D \(\phi\)
Verified Solution

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) :…