WBJEE · Maths · Functions
Let \(R\) be the set of real numbers and the functions \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be defined by \(f(x)=x^{2}+2 x-3\) and \(g(x)=x+1 .\) Then, the value of \(x\) for which \(f(g(x))=g(f(x))\) is
- A -1
- B 0
- C 1
- D 2
Answer & Solution
Correct Answer
(A) -1
Step-by-step Solution
Detailed explanation
According to question, \[ f(g(x))=g(f(x)) \] \(\Rightarrow \quad f(x+1)=g\left(x^{2}+2 x-3\right)\) \(\Rightarrow \quad(x+1)^{2}+2(x+1)-3=x^{2}+2 x-3+1\) \(\Rightarrow \quad x^{2}+1+2 x+2 x+2-3=x^{2}+2 x-2\) \(\Rightarrow \quad x^{2}+4 x=x^{2}+2 x-2\)…
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