WBJEE · Maths · Functions
If \(f(x)=2^{100} x+1, g(x)=3^{100} x+1\), then the set of real numbers \(x\) such that \(f[g(x)\}=x\) is
- A emply
- B a singleton
- C a finite set with more than one element
- D infinite
Answer & Solution
Correct Answer
(B) a singleton
Step-by-step Solution
Detailed explanation
Given, \(\quad f(x)=2^{100} \cdot x+1\) \(g(x)=3^{300} \cdot x+1\) Now, \(f\{g(x)\}=x\) \(\Rightarrow \quad f\left(3^{100}. x+1\right)=x\) \(\Rightarrow \quad 2^{100}\left\{3^{100} \cdot x+1\right\}+1=x\) \(\Rightarrow \quad 6^{100} \cdot x+2^{100}+1=x\)…
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