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what is period of f(x) which follows relation f(2x +3) + f(2x + 7) =2. my ans is coming to be 8 but in my book it is given to be 4.
Hi Manuj,
4 & 8 are both incorrect. It must be 16.
Lets see how.....
In the equation given, replace x by "x-3/2".
So we have f(2x) + f(2x+4) = 2.
Now replace x by "x+2"
So we have f(2x+4) + f(2x+8) = 2.
Subtract these two equations, and we get f(2x+8) = f(2x).
So the period of f(2x) is 8.
Hence the period of f(x) = f[1/2(2x)] is 8/(1/2) = 16.
So 16 is the period of f(x).
Hope it helps.
Wish you all the best.
Regards,
Ashwin (IIT Madras).
i understood ur solution but cant we replace x by x/2 in equation f(2x)=(f2x +8).
If the period of f(x) is T, then the period of f(ax+b) is T/|a|.
Hence when you change the co-efficient of x, then the period will change accordingly.
So you can replace x by x+a with remaining same, but not x by ax.
If you replace x by ax, then period will change. ------- (an important concept)
Hence the period of f(x) is 16.
With Regards,
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