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
f(a+b)=f(a)+f(b)
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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.
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...
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...
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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: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
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
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