Question

If f(x+y) = f(x) . f(y) , then

• A. $f\left(x\right)=a^{kx}$
• B. $f\left(x\right)=0$
• C. $f\left(x\right)=kx$
• D. $f\left(x\right)=x^n$

Answer 1

Answer: (A), (B)

$f\left(x\right)=0$

Since this is a more than one correct answer question, we will go through each of the options and check if it satisfies the given conditions

$f\left(x\right)=a^{kx}$

$\Rightarrow$ $f(x+y)=a^{k(x+y)}=a^{kx}.a^{ky}$

$\Rightarrow$ f(x) . f(y)

So, one of the functions which satisfies the given condition is $a^{kx}$

B. f(x) = 0 also satisfies the given conditions

If we go through other options, we will find that they don’t satisfy the given condition