functions problem really need help!!!?

Question

The function f is linear and satisfies f(d+1)-f(d)=3 for all real numbers d. What is f(3)-f(5)?

Answer 1

Reverse the direction
f(3) - f(5) = - [ f(5) - f(3) ]

We do not know what f(5) - f(3) is, but we do know what
f(5) - f(4) is (it is 3) and we do know what f(4)-f(3) is (also 3).

f(5)-f(3) = f(5)-f(4)+f(4)-f(3)

(we subtracted, then added f(4), which does not change our equation, because f(4)-f(4) = 0 )

We now have:
- { [f(5)-f(4)] + [f(4)-f(3)] }
-{ 3 + 3 } = -6

Answer 2

When you say that function f is linear, all you are telling me is that there are no exponents higher than 1 involved. That makes it a matter of:
multiplying out f(d+1) and f(d).
f(d +1) is distributed so that the answer is fd+f
f(d) multiplied out is just fd.
So now you have fd +f - fd =3
fd and the -fd give you 0 and all you have left is f=3
if f is 3, then substitute the value 3 in the final part of your question:
3(3)-3(5)
9-15=-6

Answer 3

If f is linear,
f(x + y) = f(x) + f(y)

Then f(d + 1) = f(d) + f(1)

That means that f(1) = 3
So, f(2) = f(1+1) = 6

So, f(3) - f(5) = 9 -15 = -6, which is your answer.

Answer 4

Use d=4 and get f(5) - f(4) = 3 or f(4) = f(5) - 3
Use d=3 and get f(4) - f(3) = 3 or f(3) = f(4) - 3

Put them together: f(3) = [f(5) - 3] - 3
And f(3) - f(5) = -6

Answer 5

given that,

f(d+1)-f(d)=3
or, f(d)+f(1)-f(d)=3
so, f(1)=3

It implies that,

f(3)=9 and
f(5)=15

s0, f(3)-f(5)=9-15
or, f(3)-f(5)= -6

Thats it.

Answer 6

f(4)-f(3) = f(5)-f(4)=3
f(4)-f(3) + f(5)-f(4)= 3+3
f(5)-f(3)=6
multiply by -1
f(3)-f(5)=-6

Answer 7

help me help me