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Let f : R -> R is a function satisfying...

Let `f : R -> R` is a function satisfying `f(2-x) = f(2 + x) and f(20-x)=f(x),AA x in R`. On the basis of above information, answer the following questions If `f(0)=5`, then minimum possible number of values of x satisfying `f(x) = 5`, for `x in [10, 170]` is

A

21

B

12

C

11

D

22

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.
Given `f(0)=5.`
` :. f(0)=f(16)=f(32)= ...=f(160)=5`
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