{ . } denotes the fractional part function and [.] denotes the greatest integer function. Now, match the following lists:

Answer

`a to s; b to r; c to s; d to p`

Explanation

a. `f(x)=e^(cos^(4)pix+x-[x]+cos^(2)px)`
`cos^(2)pi x " and " cos^(4)pi x` have period 1.
`x-[x]={x}` has period 1.
Then the period of `f(x)` is 1
b. `f(x)=cos 2pi {2x}+sin 2pi{2x}`
The period of {2x} is 1/2. Then the period of `f(x)` is 1/2.
c. Clearly, `tan pi[x]=0 AA x in R` and the period of `sin 3pi{x}` is equal 1.
d. `f(x)=3x-[3x+a]-b=3x+a-[3x+a]-(a+b)`
`={3x+a}-(a+b)`
Thus, the period of `f(x)` is 1/3.