(
for each pair of functions f and g below, find f (g(x)) and g
then, determine whether f and g are inverses of each other.
simplify your answers as much as possible.
(assume that your expressions are defined for all x in the domain of the composition.
you do not have to indicate the domain.)
(a) f(x) = * =
(b) f(x) = 2x
8(x) = 2x + 5
g(x) = 2x
xs ?
f(g(x)) = 0
f($(x)) = 0
8v(x)) = 0
8((x) =
0
f and g are inverses of each other
f and g are not inverses of each other
f and g are inverses of each other
f and g are not inverses of each other

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.

how am i supposed to answer

step-by-step explanation:

a. is correct