The function `f(x) = 3^(sin^(2)pi + sin^(4) pi x + x-[x])` where [x] denotes the greatest interger less than or equal to x, isA. a periodic function with period 1B. a periodic function with period 2C. a periodic function with period ` (1)/(2)`D. not a periodic function

The function `f(x) = 3^(sin^(2)pi + sin^(4) pi x + x-[x])` where [x] d

1.	The function `f(x) = 3^(sin^(2)pi + sin^(4) pi x + x-[x])` where [x] denotes the greatest interger less than or equal to x, isA. a periodic function with period 1B. a periodic function with period 2C. a periodic function with period ` (1)/(2)`D. not a periodic function
Answer» Correct Answer - A We have `sin^(2) pi x + sin^(4) pi x` `=(1)/(2) {1-cos 2 pi x} +(1)/(8) {3-4 cos 2 pi x + cos 4 pi x}` `=(7)/(8) - cos 2 pi x +(1)/(8) cos 4 pi x` Clearly, it is a peridic function equal to LCMof `(2pi)/(2pi)` and `(2pi)/(4)` i.e., 1. Also, `x - [x]` is periodic with period 1. Hence, `f(x)` is periodic with period 1.

Discussion

No Comment Found

Related InterviewSolutions

Find the equivalent definition of`f(x)=m a xdot{x^2,(-x)^2,2x(1-x)}w h r e0lt=xlt=1`A. `f(x)={{:(x^(2),0 le x le 1//3),(2x(1-x),1//3 le x le 2//3),((1-x)^(2), 2//3 le x le 1):}`B. `f(x)={{:((1-x)^(2), 0 le x le 1//3),(2x(1-x),1//3 le x le 2//3),(x^(2), 2//3 le x le 1):}`C. `f(x)={{:(x^(2),0 le x le 1//2),((1-x)^(2),1//2 le x le 1):}`D. none of these
Domain of the function `f(x) = log(sqrt(x-4)+sqrt(6-x))`A. [4,6]B. `(-oo,6)`C. `(2,3)`D. none of these
If `f(x)=sin(logx)` then `f(xy)+f(x/y)-2f(x)cos(logy)=` (A) `cos(logx)` (B) `sin(logy)` (C) `cos(log(xy))` (D) 0A. `-1`B. `0`C. 1D. none of these
The domain of definition of the function `f(X)=x^((1)/(log_(10)x))`, isA. `(0,1) cup (1,oo)`B. `(0,oo)`C. `[0,oo)`D. `[0,1) cup (1,oo)`
The domain of definition of the function `f(x)=log_(3){-log_(4)((6x-4)/(6x+5))}` , isA. `(2//3,oo)`B. `(-oo,-5//6) cup (2//3,oo)`C. `[2//3,oo)`D. `(-5//6,2//3)`
The set of all real values of x for which the funciton `f(x) = sqrt(sin x + cos x )+sqrt(7x -x^(2) - 6)` takes real values isA. `[1, 3pi//4] uu [7pi//4, 6]`B. `[1, 3pi//4]uu [ 6- pi//4, 6]`C. `[1, 6]`D. none of these
The equivalent definition of `f(x)=||x|-1|`, isA. `f(x)={{:( -x-1, x le -1),(x+1, -1 lt x le 0),( 1-x, 0 le x le 1), (x-1,x le 1):}`B. `f(x)={{:(x-1,x le -1),(x+1,-1 lt x le 0),(x-1, 0 le x le 1),(x+1, x ge 1):}`C. `f(x)={{:( x+1, x ge 0), (x+1, x le0):}`D. none of these
`f(x)={(4, xlt-1) ,(-4x,-1lt=xlt=0):}` If `f(x)` is an even function in R then the definition of `f(x)` in `(0,oo)` is:(A) `f(x)={(4x, 0ltxle1),(4, xgt1):}` (B) `f(x)={(4x, 0ltxle1),(-4, xgt1):}` (C) `f(x)={(4, 0ltxle1),(4x, xgt1):}` (D) `f(x)={(4, xlt-1),(-4x, -1lexle0):}`A. `f(x)={:(4x, 0 lt x le 1),(4, x gt 1):}`B. `f(x)={{:(4x, 0 lt x le1),(-4, x gt 1):}`C. `f(x)={{:(4, 0 lt x le 1),(4x,x gt 1):}`D. none of these
If a funciton f(x) is defined for ` x in [0,1]`, then the function f(2x+3) is defined forA. `x in [0,1]`B. `x in [-3//2,-1]`C. `x in R`D. `x in [-3//2,1]`
If `b^2-4ac=0,a>0` then the domain of the function `f(x)=log(a x^3+(a+b)x^2+(b+c)x+c)` is :A. `R-{-(b)/(2a)}`B. `R-{{-(b)/(2a)} cup {x|x ge-1|}}`C. `R-{{-(b)/(2a)}cap(-oo,-1]}`D. none of these

The function `f(x) = 3^(sin^(2)pi + sin^(4) pi x + x-[x])` where [x] denotes the greatest interger less than or equal to x, isA. a periodic function with period 1B. a periodic function with period 2C. a periodic function with period ` (1)/(2)`D. not a periodic function

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment