Question

If f(x+5)=f(x) for all values of x, then f(x)=0 for how many different values of x between 0 and 12?

Answer 1

@jim_thompson5910

Answer 2

what f(x+5)=f(x) means is that the function repeats itself every 5 units (so the period of this function is 5)

what this means is that if f(x) = 0, then this could happen at most 3 times (at x = 0, x = 5 and x = 10)

however, it could easily be twice (say at x = 3 and x = 8 since x = 13 is out of the interval)

there's no way it could happen exactly once (go ahead and try different x values and you'll see this is true)

however, it's possible that f(x) = 0 is not true for any values of x, so there could easily be no solutions for f(x) = 0

Answer 3

There's a strange graph to go with this, if you'd like to see it.

A) Eight
B) Nine
C) Ten
D) Eleven
E) Twelve

Answer 4

go ahead and post it