f(a+b)=f(a)+f(b)

dzelkas wrote:can someone help me explain how to solve this problem?

For which of the following functions is f(a+b)=f(a)+f(b) for al positive numbers a and b?

a) f(x)=x^2

b) f(x)=x+1

c) f(x)= sq root of x

d) f(x)=2/3

e) f(x)=-3x

I will go by each option:

from (A) : f(a)=a^2 , f(b)=b^2 f(a+b)=(a+b)^2 which is not equal to (a^2) + (b^2) [ f(a) + f(b) ]

from (B): f(a)=a+1 , f(b)=b+1 , f(a+b)=a+b+1 which is not equal to (a+1)+(b+1) = a+b+2 [ f(a) + f(b) ]

from (C): f(a)= sqrt(a) , f(b)=sqrt(b) , f(a+b) = sqrt(a+b ) which is not equal to sqrt(a)+sqrt(b) [ f(a) + f(b) ]

from (D) : f(a)=2/3 , f(b) = 2/3 , f(a+b)=2/3 which is not equal to 2/3 + 2/3 [ f(a) + f(b) ]

from (E): f(a)= -3a , f(b)= -3b , f(a+b)= -3(a+b)=(-3a) + (-3b)=f(a) + f(b)

Hence, (E) will be my answer.

Thanks for that - I had a similar question and had no clue where to start.

I'm still lost on this one..how do you rephrase what this question is asking?

For which of the following functions is f(a+b)=f(a)+f(b) for all positive numbers a and b?

Can you intepret it as asking for all of the functions below, which function, that is the sum of 2 numbers produces an output that is equal to the sum of those 2 numbers' functions? I'm confused...just trying to put this math into simple english...

dzelkas wrote:can someone help me explain how to solve this problem?

For which of the following functions is f(a+b)=f(a)+f(b) for al positive numbers a and b?

a) f(x)=x^2

b) f(x)=x+1

c) f(x)= sq root of x

d) f(x)=2/3

e) f(x)=-3x

We need to determine when f(a + b) = f(a) + f(b). We can determine the correct answer choice by substituting numerical values for a and b. We could use any two values for a and b, but for simplicity, let’s choose a = 1 and b = 2. The function now looks like this:

f(1 + 2) = f(1) + f(2)

f(3) = f(1) + f(2)

So, we must determine which answer choice has f(3) equal to the sum of f(1) and f(2).

Let’s evaluate each answer choice.

A) f(x) = x^2

f(3) = 3^2 = 9

f(1) = 1^2 = 1

f(2) = 2^2 = 4

Since 9 does not equal 1 + 4, choice A is not correct.

B) f(x) = x + 1

f(3) = 3 + 1 = 4

f(1) = 1 + 1 = 2

f(2) = 2 + 1 = 3

Since 4 does not equal 3 + 2, choice B is not correct.

C) f(x) = √x

f(3) = √3

f(1) = √1 = 1

f(2) = √2

Since √3 does not equal 1 + √2, choice C is not correct.

D) f(x) = 2/x

f(3) = 2/3

f(1) = 2/1 = 2

f(2) = 2/2 = 1

Since 3/2 does not equal 1 + 2, choice D is not correct.

E) f(x) = -3x

f(3) = -3(3) = -9

f(1) = -3(1) = -3

f(2) = -3(2) = -6

Since -9 equals -3 + (-6), choice E is correct.

Answer: E