Question

Let $f$ be an even periodic function with period $2$ and $f\left(x\right)=x\forall x\in [0,1].$ Then $f\left(3.14\right)$ equals

• A. $-3.14$
• B. $-0.14$
• C. $0.14$
• D. $0.86$

Answer 1

The correct option is D $0.86$

$f\left(x\right)=xforallxϵ[0,1]\because fbeaperiodof2.\therefore f(x+2)=x=f(x+4),xϵ[0,1]f\left(3.14\right)=f(4-0.86)=f\left[\right(2\times 2)+(-0.86\left)\right]=0.86\left[becausef\right(x)=f(-x\left)\right]$