Question

A function f:R-->R is defined as

f (x+1)= f(x) + 2x +3, f (0)=1 .

Find f (2020).

Answer 1

Step-by-step explanation:

What I did:

f(2x+3)+f(2x+7)=2.........(1)

Replacing x with x−1 in (1),

f(2x+1)+f(2x+5)=2.........(2)

And replacing x with x+1 in (1),

f(2x+5)+f(2x+9)=2.........(3)

Subtracting (2) from (3), I get

f(2x+1)=f(2x+9)

Since x∈R⟺2x∈R, replace 2x with x to get

f(x)=f(x+8)⟹t=8

But sadly, my textbook's answer is t=4.