Find the indicated values where g(t)=t2-t and f(x) =1+x
g(f(0)) + f(g(0))

Choice A is correct

Step-by-step explanation:

The composite function g(f(x)) will be given by (1+x)^2 -(1+x). Substituting x with zero yields g(f(0)) =0. On the other hand, the composite function f(g(t)) will be given by 1+t^2-t. Substituting t with zero yields f(g(0)) =1. The sum is thus equal to 1

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

14.29%

step-by-step explanation: