Question

Can someone explain how to solve this?
A function f may have the property that, for all numbers a and b in the domain of f.
f(a)+ f(b)=f(a+b)
Evaluate and check whether each of the following functions has the property described above. If it does not, give an example to show that it does not.

1.f(x)=x superscript 2
2.f(x)= 2x
3.f(x)=|x|
4.f(x)=5x+1
5.What must be true about the numbers m and/or b in order for a function of the form f(x)=mx+b to have the property above?

Answer 1

Sure, so just simply plug in stuff to see if it gives you true statements or not. So for example:

f(x)=2x we just do

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

now you plug in

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

2a+2b=2a+2b

that is true, so it's got the property we wanted.

Answer 2

What do I plug the number into- the a and b?

Answer 3

Oh- I think I understand. So, for the first one, I would have f(2^2)+f(2^2)=f(2^2+2^2)?

Answer 4

Kind of. So whatever is in the parenthesis is what you replace x with for f(x)

So f(x)=x^2 and we are checking for a, b, and (a+b). So start with

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

So take that f(a) and replace it with a^2 since they're equal.

Answer 5

So if I give you the function:

f(x)=4x^3

then

f(elephants)=4(elephants)^3

Answer 6

So I don't replace the function, just the variables?