Question

Given f(x) defined on f: R $\to$ R is a periodic function with the fundamental period 2 then f(3) is not equal to -

• A. f(2)
• B. f(9)
• C. f(5)
• D. f(-1)

Answer 1

The correct option is A

f(2)

We know that for a periodic function ,

f(x) = f(x +T) , T is the period of the function

Here, we have period as 2

f(x) = f(x +2)

or f(3) = f(3+2) = f(5)

& f(5) = f(7) = f(9)

On the negative side of x-axis if we take…

f(3) = f(3-2) = f(1)

f(1) = f(1-2) = f(-1)

so, f(3) = f(5)= f(9) = f(-1)

And the option which is not equal to f(3) is f(2) which is A.