TS EAMCET · Maths · Functions
Let \(f\) be a non-zero real valued continuous function satisfying \(f(x+y)=f(x) \cdot f(y)\) for all \(x, y \in \mathbb{R}\). If \(f(2)=9\), then \(f(6)\) is equal to
- A \(3^2\)
- B \(3^6\)
- C \(3^4\)
- D \(3^3\)
Answer & Solution
Correct Answer
(B) \(3^6\)
Step-by-step Solution
Detailed explanation
\[ \because \quad f(x+y)=f(x) f(y), \forall x, y \in R \] Put \(x=y=1\), we get \[ \begin{aligned} & f(2)=f(1) \cdot f(1)=9 \quad[\because f(2)=9] \\ & \Rightarrow \quad f(1)^2=9 \Rightarrow f(1)=3 \\ & \end{aligned} \] Now, put \(x=2\) and \(y=1\) in Eq. (i), we get…
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