Please Check my work / Answer: Let f(x) be a function with 2 properties:

[dmatzick]

a) for any 2 real numbers x and y, f(x+y) = x+f(y), and
b) f(0) = 2
FIND the f(1998)

So this is what I did:
I chose x = 1 & y = 0 and plugged into the function:
f(1+0) = 1 + f(0)
f(1) = 1+2
f(1) = 3

and I did it again for x = 2 and y = 0 and got f(2) = 4
and again for x = 3, y = 0 and got f(3) = 5

Seeing a pattern, I plugged in x = 1998 & y = 0
f(1998) = 1998 + f(0)
f(1998) = 1998 + 2
f(1998) = 2000

Is that correct?

Thank you!!

 

[mmm4444bot]

a) for any 2 real numbers x and y, f(x+y) = x+f(y), and
b) f(0) = 2
FIND the f(1998)

So this is what I did:
I chose x = 1 & y = 0 and plugged into the function:
f(1+0) = 1 + f(0)
f(1) = 1+2
f(1) = 3

and I did it again for x = 2 and y = 0 and got f(2) = 4
and again for x = 3, y = 0 and got f(3) = 5

Seeing a pattern, I plugged in x = 1998 & y = 0
f(1998) = 1998 + f(0)
f(1998) = 1998 + 2
f(1998) = 2000

Is that correct?

Yes.

The function input is: x+y

The function output is: x+y+2

In other words, the output is always two greater than the input. :cool:

 

[dmatzick]

YAY! Thank you!

Thank you!