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)

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

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

Step-by-step explanation:

Given :

To Find: The formula and domain for  and  

Solution:

The domain is all Real numbers except because if    the denominator would be zero and you cannot divide by zero.

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

The domain is all Real numbers except because if    the denominator would be zero and you cannot divide by zero.

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

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: