Question

HELP ASAP

Given s(x) = 3x - 6 and t(x) = 6 - 3x.

find the simplified formula and domain for
v(x)=(s/t) and w(x)=(t/s)(x)

Answer 1

1) Set the denominator equal to zero.

2) Solve for x.

3) Restrict those values of x from the domain.

So, you get: 6 - 3x = 0 which implies 3x = 6. So, x = 2. When you restrict, you find: x ≠ 2.

For w, you get: 3x - 6 = 0 which implies 3x = 6. So, x = 2. When you restrict, you find: x ≠ 2.

So, what do these functions really look like? They are almost identical to the line y = -1 except...what?

There is a hole when x = 2 where the function is not defined.

Explanation:

this is 100% correct

Answer 2

v(x)=(s/t)
= (3x - 6) / (-3x+6)
= [3(x-2)] / [-3(x-2)] --> 3 is factored out
= 1/-1 ---> common terms are cancelled out.
= -1 ---> This is the simplified formula.

To find the domain, we equate the denominator to 0.
-3x+6 = 0
3x = 6
x = 2
Domain: all values except 2.

w(x)=(t/s)(x)
= (-3x+6)x / (3x-6)
= [-3x(x-2)] / [3(x-2)] --> 3 is factored out
= -x --> The common terms are cancelled out. This is the simplified formula.

Solving for domain:
3x-6 = 0
3x = 6
x = 2
Domain: all values except 2.