Let `f(x)`be periodic and `k`be a positive real number such that `f(x+ – InterviewSolution

1.	Let `f(x)`be periodic and `k`be a positive real number such that `f(x+k)+f(x)=0fora l lx in Rdot`Prove that `f(x)`is periodic with period `2kdot`
Answer» We have `f(x+k)+f(x)=0 AA x in R` or ` f(x+k)= -f(x) AA x in R` Put `x=x+k.` Then, or `f(x+2k)= -f(x+k) AA x in R` or ` f(x+2k) = f(x), AA x in R " "[ "As "f(x+k)= -f(x)]` which clearly shows that f(x) is periodic with period 2k.

Discussion

No Comment Found

Related InterviewSolutions

One cubic meter piece of copper is melted and recast into a bar 36 meters long with a square cross-sectional area. An exact cube is cut off from this bar. The cost of this cube, if 1 m3 of copper costs Rs.216 will be :
If `(x-2,y+5)=(2,(1)/(3))` are two equal ordered paris, then `x=4, y=(-14)/(3)`
If `f(x)=(4x+3)/(6x-4), x !=2/3,`show that `fof(x)=x`for all `x!=2/3dot`What is the inverse of `f?`
The number of roots of `x^2-2=[sinx],w h e r e[dot]`stands for the greatest integer function is0 (b)1 (c) 2(d) 3.
Domain of the function, `f(x)=[log_10 ((5x-x^2)/4)]^(1/2)` isA. `-oo lt x lt oo`B. `1 le x le 4 `C. `4 le x le 16`D. ` -1 le x le 1`
The period of `f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x ,`where `n in N ,`is (where `[dot]`represents greatest integer function).`n`(b) 1(c) `1/n`(d) none of theseA. nB. 1C. `(1)/(n)`D. none of these
The derivative of `log_10 x` is ?
Find the value of x `tan^-1 ((x-1)/(x+1)) + tan^-1 ((2x-1)/(2x+1)) = tan^-1 (23/36)`
Let [ ] represents the greatest integer function and `[ x^3 + x^2 + 1 + x] = [ x^3 + x^2 + 1] + x`. The number of solution of the equation log|[x]| = 2 - |[x ]|
a bag contains lemon flavored candies only. Malini takes out one candy without looking into the bag . What is the probability that she takes out(i) an orange flavored candy ? (ii) an lemon flavored candy ?