Question

Given s(x) = 2x - 3 and t(x) = 5x + 4. Find the formula and domain for v(x) = s (x) / t (x) and w(x) = t (x) / s (x)

Answer 1

V(x) = (2x - 3)/(5x + 4)
The domain is all Real numbers except x = -4/5, because if x = -4/5 the denominator would be zero and you cannot divide by zero.
{x | x ∈ R, x ≠ -4/5}

w(x) = (5x + 4)/(2x - 3)
similarly, x ≠ 3/2
so, {x| x ∈ R, x ≠ 3/2}

Answer 2

Answer:

$v(x) = \frac{2x-3}{5x+4}$

Domain of v(x) is {x | x ∈ R, x ≠ -4/5}

$w(x) = \frac{5x+4}{2x-3}$

Domain of w(x) is {x | x ∈ R, x ≠ 3/2}

Step-by-step explanation:

Given : $s(x) = 2x - 3$

            $t(x) = 5x + 4$

To Find: The formula and domain for $v(x) = \frac{s (x)}{t(x)}$  and   $w(x) = \frac{t (x)}{ s (x)}$

Solution:

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

$v(x) = \frac{2x-3}{5x+4}$

The domain is all Real numbers except $x=\frac{-4}{5}$ because if $x=\frac{-4}{5}$    the denominator would be zero and you cannot divide by zero.

So, Domain of v(x) is {x | x ∈ R, x ≠ -4/5}

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

$w(x) = \frac{5x+4}{2x-3}$

The domain is all Real numbers except $x=\frac{3}{2}$ because if $x=\frac{3}{2}$    the denominator would be zero and you cannot divide by zero.

So, Domain of w(x) is {x | x ∈ R, x ≠ 3/2}