Let `f:R to R ` be a function satisfying `f(2-x)=f(2+x) and f(20-x)=f(x) AA x in R.` For this function `f`, answer the following. If `f(2) ne f(6),` then theA. fundamental period of `f(x) " is " 1`B. fundamental period of `f(x) " may be " 1`C. period of `f(x)` cannot be 1D. fundamental period of `f(x) " is " 8`

Let `f:R to R ` be a function satisfying `f(2-x)=f(2+x) and f(20-x)=f(

1.	Let `f:R to R ` be a function satisfying `f(2-x)=f(2+x) and f(20-x)=f(x) AA x in R.` For this function `f`, answer the following. If `f(2) ne f(6),` then theA. fundamental period of `f(x) " is " 1`B. fundamental period of `f(x) " may be " 1`C. period of `f(x)` cannot be 1D. fundamental period of `f(x) " is " 8`
Answer» Correct Answer - C `f(2-x) =f(2+x) " (1)" ` Replace x by `2-x. " Then " f(x)=f(4-x) " (2)" ` Also, given `f(20-x)=f(x) " (3)" ` From (1) and (2), `f(4-x)=f(20-x).` Replace x by `4-x. " Then " f(x)=f(x+16).` Hence, the period of `f(x)` is 16. If 1 is a period, then `f(x)=f(x+1) AA x in R` `or f(2)=f(3)=f(4)=f(5)=f(6)` which contradicts the given hypotheses that `f(2) ne f(6).` Therefore, 1 cannot be period of `f(x)`.