WBJEE · Maths · Sequences and Series
Let \(f: R \rightarrow R\) be such that \(f\) is injective and \(f(x) f(y)=f(x+y) \quad\) for \(\quad\) all \(\quad x, y \in R, \quad\) if \(f(x), f(y)\) and \(f(z)\) are in \(G P,\) then \(x, y\) and \(z\) are in
- A AP always
- B GP always
- C AP depending on the values of \(x, y\) and \(z\)
- D GP depending on the values of \(x, y\) and \(z\)
Answer & Solution
Correct Answer
(A) AP always
Step-by-step Solution
Detailed explanation
Let the function, \(f(x)=a^{kx}\) Which define in \(f: R \rightarrow R\) and injective also. Now, we have \[ f(x) f(y)=f(x+y) \] \(\Rightarrow\) \(a^{k x} \cdot a^{k y}=a^{k(x+y)}\) \(\Rightarrow\) \(a^{k(x+y)}=a^{k(x+y)}\) \(\because \quad f(x), f(y)\) and \(f(z)\) are in GP…
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