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

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 $w ( x ) = \frac { t ( x ) } { s ( x ) }$.

$\frac{3x-6}{6-3x}=\frac{3(x-2)}{3(2-x)}=\frac{x-2}{2-x}=\frac{x-2}{-(x-2))}=-1$

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

$\frac{6-3x}{3x-6}=\frac{3(2-x)}{3(x-2)}=\frac{2-x}{x-2}=\frac{2-x}{-(-x+2)}=\frac{2-x}{-(2-x)}=-1$

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

Answer 2

ANSWER

v(x)=-1

Domain: (-∞,2)U(2,+∞)

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

$v(x) =( \frac{s}{t} )(x)$

$v(x) = \frac{s(x)}{t(x)}$

$v(x) = \frac{3x - 6}{6 - 3x}$

This function is defined if and only if

$6 - 3x \ne0$

$x \ne2$

Hence the domain is:

$x \ne2$

We now simplify to obtain;

$v(x) = \frac{ - (6 - 3x )}{6 - 3x} = - 1$