<h2>
Answer with explanation:</h2>
It is given that:
f: R → R is a continuous function such that:
∀ x,y ∈ R
Now, let us assume f(1)=k
Also,
( Since,
f(0)=f(0+0)
i.e.
f(0)=f(0)+f(0)
By using property (1)
Also,
f(0)=2f(0)
i.e.
2f(0)-f(0)=0
i.e.
f(0)=0 )
Also,
i.e.
f(2)=f(1)+f(1) ( By using property (1) )
i.e.
f(2)=2f(1)
i.e.
f(2)=2k
f(m)=f(1+1+1+...+1)
i.e.
f(m)=f(1)+f(1)+f(1)+.......+f(1) (m times)
i.e.
f(m)=mf(1)
i.e.
f(m)=mk
Now,
Also,
i.e.
Then,
(
Now, as we know that:
Q is dense in R.
so Э x∈ Q' such that Э a seq belonging to Q such that:
)
Now, we know that: Q'=R
This means that:
Э α ∈ R
such that Э sequence such that:
and
( since belongs to Q )
Let f is continuous at x=α
This means that:
This means that:
This means that:
f(x)=kx for every x∈ R
Answer:
13y + 1
Step-by-step explanation:
8y + 5y = 13y
3 - 2 = 1
13y + 1
Answer:
D
Step-by-step explanation:
Answer:
y= x -1.25
Step-by-step explanation:
Use slope= y2-y1/x2-x1
(13.75, 12.50), (3.25 , 2.00)
12.50 -2.00/ 13.75 -3.25
10.50/ 10.50
slope= 1
Substitute into y=mx+b
12.50= 1(13.75) +b
b= -1.25
y= x -1.25