Q255 / 270 · NDA 2015 (Phase 2) · Mathematics

$f(x y)=f(x)+f(y)$ is true for all

  • A
    Polynomial functions f
  • B
    Trigonometric functions f
  • C
    Exponential functions f
  • Correct answer
    D
    Logarithmic functions f

Solution

$\begin{aligned} & \text { Let } \mathrm{f}(\mathrm{x})=\log \mathrm{x} \\ & \therefore \mathrm{f}(\mathrm{y})=\log \mathrm{y} \\ & \& \mathrm{f}(\mathrm{xy})=\log (\mathrm{xy})=\log \mathrm{x}+\log \mathrm{y} \\ & \Rightarrow \mathrm{f}(\mathrm{xy})=\mathrm{f}(\mathrm{x})+\mathrm{f}(\mathrm{y})\end{aligned}$

Hence, the correct answer is option: 'D'.

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