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If f: RvecR is a function satisfying the...

If `f: RvecR` is a function satisfying the property `f(2x+3)+f(2x+7)=2AAx in R ,` then find the fundamental period of `f(x)dot`

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The correct Answer is:
8
`f(2x+3)+f(2x+7)=2 " (1)" `
Replacing x by `x+2,f(2x+7)+f(2x+11)=2 " (2)" `
From (1) -(2), we get
`f(2x+3)-f(2x+11)=0`
or `f(2x+3)=f(2x+11)`
Replace `2x+3` by x. Then
`f(x)=f(x+8)`
Hence, fundamental period of `y=f(x)` is 8`.
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