IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

(5)

1.period of iog(sin inverse (x-greatest integer x)

2.range of x//x/

3.f(2x+3)+f(2x+7)=2 ,

then period of f(x).

pannaguma

2]
D = R- {0}
R = 1, -1.

pannaguma

1]D = R - Integers.
period should be 1.
since 0<={x}<1

ayshwarya

wats d ans for d 3rd 1

ayshwarya

is it 4 yaar if s den rate me i will giv d soln

ayshwarya

sorry yar fr my delay ok let me answer

4 des kind of quesns der is a shortcut if it is in d form f(ax+_b)+_f(ax+_c) =k

den its period may b (c-b)

uday_zingtudor

f(2x+3) + f(2x+7) = 2.............................(I)

replacing x by x+2

f(2x+7) + f(2x+11) = 2...........................(II)

that implies

(II) - (!) = f(2x+11) - f(2x+3) = 0

f(2x+3) = f(2(x+4) +3)

Therefore the period is '4'

~Cheerio!!

edit: dint see all the questions!!!

For the first one, the function {x} has a period '1'.The period is dependent only on that function.So the period is 1.

The second question has already been answered well by pannaguma

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