What is the range of the function g(x) = 3x^2 - 6x + 3 when the domain is defined as the set of integers, x, such that 0< =x< =4? show all work.

Range is  3 <= g(x) <= 27.

Step-by-step explanation:

The range  is the values of g(x) for the given domain.

When x = 0 g(x) = 3(0)^2 - 6(0) + 3 = 3.

When x = 4 g(x) = 3(4)^2 - 6(4) + 3 =  27.

70

step-by-step explanation:

2*5=10

4*15=60

60+10=

70

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)