Thread: function equation functions

Let f be a function dened on the set of integers such that f(1) = 5
and f(x + 1) = 2f(x) + 1 for all integers x. What is the value of
f(7) - f(0)?

i bet the answer is 381 but i couldn't make how to the solution is done.

Originally Posted by rcs

Let f be a function de ned on the set of integers such that f(1) = 5
and f(x + 1) = 2f(x) + 1 for all integers x. What is the value of
f(7) - f(0)?

i bet the answer is 381 but i couldn't make how to the solution is done.

Since you know f(1) you can calculate f(2). Knowing f(2) you can calculate f(3) etc. So you can get f(7). And obviously f(1) = 2f(0) + 1 => f(0) = ....

Originally Posted by rcs

Let f be a function dened on the set of integers such that f(1) = 5
and f(x + 1) = 2f(x) + 1 for all integers x. What is the value of
f(7) - f(0)?

i bet the answer is 381 but i couldn't make how to the solution is done.

How did you get 381? A guess?

a friend of mine told me that it is 381,,, but she couldnt show to me how she solved it,,, that is why i just guessed it. hope i could get the right flow of the solution. thanks

Look at this website.

Hello, rcs!

If you can read the problem, you can baby-talk your way through it.

The first term is 5.
Each subsequent term is twice the preceding term, plus 1.


We have:

. .


What is ?

Since , we have: .


Therefore: .

thanks you so so much Soroban!!! ilove you all here! i can now have a good night sleep