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).

Approved

i understood ur solution but cant we replace x by x/2 in equation f(2x)=(f2x +8).

Hi Manuj,

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,

Ashwin (IIT Madras).