Question

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

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

Answer 1

v(x)=-1

Domain: (-∞,2)U(2,+∞)

Step-by-step explanation

We have the given function

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

We want to find the simplified formula and domain for

`v(x) =( (s)/(t) )(x)`

`v(x) = (s(x))/(t(x))`

`v(x) = (3x - 6)/(6 - 3x)`

This function is defined if and only if

`6 - 3x \\e0`

`x \\e2`

Hence the domain is:

`x \\e2`

We now simplify to obtain;

`v(x) = ( - (6 - 3x ))/(6 - 3x) = - 1`

Answer 2

Answer with step-by-step explanation:

We are given the following two functions:

`s(x) = 3x - 6`

`t(x) = 6 - 3x`

We are to find the simplified formula and domain for
`v ( x ) = \frac { s ( x ) } { t ( x ) }` and
`w ( x ) = \frac { t ( x ) } { s ( x ) }`.

`(3x-6)/(6-3x)=(3(x-2))/(3(2-x))=(x-2)/(2-x)=(x-2)/(-(x-2)))=-1`

So the domain for this function is (-∞, +∞) for v(x) = -1.

`(6-3x)/(3x-6)=(3(2-x))/(3(x-2))=(2-x)/(x-2)=(2-x)/(-(-x+2))=(2-x)/(-(2-x))=-1`

The domain of this function is (-∞, +∞) for w(x)= -1