I have no clue how to do this.A function is additive if f(a+b)f(a)+f(b) for all a and b in its domain and multiplicative if f(ab)f(a)f(b) for all a and b in its domain.Which of the following functions are additive and which are multiplicative? Justify your answers1. f(x)sqrt x2. f(x)sinx3. f(x)1/x4. f(x)e^x5. f(x)x^36. f(x)3xThanks so much!
I took math long time ago , but I will try my best. This is really simple as you need to understand the rule for it. 1-square root of X x^1/2which is additive 2-multiplicative 3-? 4? 5additive, 6-this is a additive one because f(3)+f(x), you just need to break it down I might be wrong though
It tells you in the definition what to do. Just put in some numbers, and see if they check out. No. 6 says f(x) 3x. Put a 2 and b 3. f(a) 6 and f(b) 9. So f(a) + f(b) 6 + 9 15 And f(a + b) f(5) 15. Which checks. So f(x) 3x is additive. No 1. says f(x) √x Choosing carefully, let a 9 and b 16. f(a) √9 3 ; f(b) √16 4 f(a) + f(b) 3 + 4 7 And f(a + b) f(9 + 16) f(25) 5. Which does not tally. The function is not additive. f(a) x f(b) √9 x √16 3 x 4 12 And f(a x b) f(9 x 16) f(144) √144 12 - check. The function is multiplicative. Just do the same for the rest.
