Question

A certain function f has the property that f(x+y)=
f(x)+f(y) for all values of x and y. Which of the
following statements must be true when a=b?
I. f(a+b)=2f(a).
II. f(a+b)=[f(a] to the power of 2.
III. f(b) +f(b)=f(2a)

Answer 1

this is a function problem...

Answer 2

(i) is true
f(a+b) = f(a) + f(b) = f(a) + f(a) = 2f(a)

Answer 3

f(a+b) = f(a+a) = f(a) + f(a) = 2f(a)

Answer 4

ahh, since a=b, right?

Answer 5

I. f(a+b)=2f(a) is true because f(a+b) = f(a) + f(b), since a = b, f(b) = f(a), so f(a) + f(a) = 2f(a) so I must be true.

Answer 6

all good responses

Answer 7

(iii) is also true. Just use what is given.

Answer 8

let us see

Answer 9

II. isn't true

Answer 10

And because of this, II is false.

Answer 11

a=1, b=1

Answer 12

wait

Answer 13

a=3

Answer 14

b=3

Answer 15

6 does not equal 9

Answer 16

but f(2a)

Answer 17

because

Answer 18

f(b)+f(b)=f(2b)=f(2a)

Answer 19

right?

Answer 20

Yeah.

Answer 21

ty micah

Answer 22

f(b)+f(b)=f(2b)=f(2a) is a good statement.
I'm not sure why you are using #'s like 1 and 3

Answer 23

sometimes I like to pick variables to solve the problem...

Answer 24

Usually, that's a good strategy, but you don't know what f(x) is in this case.

Answer 25

We don't know function so you can't use number as a variable. We only know that f(a + b) = f(a)+ f(b), that all.

Answer 26

Just like cruffo said.

Answer 27

ty, guys

Answer 28

next problem?

Answer 29

ok

Answer 30

Ask as many questions as you like.

Answer 31

ty