# What is the Mapping rule for the Equation using the points Cos 0,90,180,270,360 3 cos[Pi(x +2)]-1

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The map is a function that connects an element of domain with one and only one element of range.

To determine the mapping rule, put, one by one, cos `pi(x+2)` = cos 0, cos `pi(x+2)` = cos 90, cos `pi(x+2)` = cos 180,cos `pi(x+2)` = cos 270,cos `pi(x+2)` = cos 360.

cos `pi(x+2)` = cos 0 => `pi(x+2)` = 0 => x+2 = 0 => x=-2

The function is f(x) = `3cos pi(x+2) - 1` .

Substitute `cos pi(x+2) ` by cos 0 = 1 => `3cos pi(x+2) - 1 = 3-1 = 2`

Therefore, for x = -2, the value of the function is f(-2)=2.

`cos pi(x+2) = cos 90<=> cos pi(x+2) = cos (pi/2) =gt pi(x+2) = pi/2 =gt x+2 = 1/2 =gt x = 1/2 - 2 =gt x = -3/2`

Substitute `cos pi(x+2)` by `cos (pi/2) =0` => `3cos pi(x+2) - 1 = 0-1 = -1`

Therefore, for `x = -3/2` , the value of the function is `f(-3/2)=-1` .

`cos pi(x+2) = cos 180 ` <=> `cos pi(x+2)= cos pi ` =>`pi(x+2)= pi =gt x+2 = 1 =gtx = -1`

Therefore, for x = -1, the value of the function is f(-1)=-3-1=-4

`cos pi(x+2) = cos 270 ` <=> `cos pi(x+2)= cos (3pi)/2 =gt pi(x+2)= (3pi)/2 =gt x+2 =3/2 =gtx = 3/2-2 = -1/2`

Therefore, for `x = -1/2` , the value of the function is `f(-1/2)=-1`

`cos pi(x+2) = cos 360` <=> `cos pi(x+2)= cos (2pi) =gt pi(x+2)=2pi =gt x+2 =2 =gtx = 0 `

x=0 => f(0)=2

**The domain of definition of function f(x) = 3cos pi(x+2) - 1 is {-2 ; -3/2 ; -1 ; 0} and the range is {-4;-1;2}.**