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Let f:R to R be a function satisfying f...

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 about

A

symmetrical about `x=2`

B

symmetrical about `x=10`

C

symmetrical about `x=8`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
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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