Given f(x) = -8x+6 and g(x) = x^3 choose the expression for (f of g)(x)

(f o g)(x) is the composition of function where we substitute one function into other function.

So, (f o g)(x) = f( g(x) )

The given functions are f(x) = -8x+6 and g(x) = x³.

So,we need to plug in x³ for g(x) in f(x). Therefore,

(f o g)(x) = f( g(x) )

= f (x³) Replace g(x) with x³.

= -8x³ + 6 Replace x³ with x in f(x).

So, (f o g)(x) = -8x³ + 6.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.