Question

$f\left(xy\right)=f\left(x\right)+f\left(y\right)$ is true for all

• A. Polynomial functions $f$
• B. Trigonometric functions $f$
• C. Exponential functions $f$
• D. Logarithmic functions $f$

Answer 1

Answer: (D)

Logarithmic functions $f$

Solution:

Let, $f\left(x\right)=\log x$

$\therefore f\left(xy\right)=\log \left(xy\right)$ and $f\left(x\right)=\log x,f\left(y\right)=\log y$

Now, $f\left(x\right)+f\left(y\right)=\log x+\log y=\log \left(xy\right)=f\left(xy\right)$

Hence, $f\left(x\right)+f\left(y\right)=f\left(xy\right)$

Hence, D is the correct option.