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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. The graph of `y= f(x)` is not symmetrial aboutA. symmetrical about `x=2`B. symmetrical about `x=10`C. symmetrical about `x=8`D. None of these |
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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. `f(2-x)=f(2+x)` Hence, `y=f(x)` is symmetrical about `x=2`. Also, `f(20-x)=f(x)` `or f(20-(10+x))=f(10+x)` `or f(10-x)=f(10+x)` Hence, `y=f(x)` is symmetrical about `x=10`. |
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