Question

For each given pair of functions, multiply or divide as instructed. Be sure to show all the steps

required to write your answer in simplest form. Review the rubric to see how your work will be
graded.
1) f(x)=2x
g(x)=3x^3

f(x)/g(x)=?

Answer 1

`(f(x))/(g(x)) =?`

Since you know f(x) = 2x and g(x) = 3x^3, you can substitute that into the function

`(f(x))/(g(x)) =?`

`(2x)/(3x^3) =?`

When a variable(x or y) with an exponent is divided by another variable with an exponent, you subtract the exponents, only if the variables are the same.

For example:

`(x)/(y)` Since the variables on the top and bottom are not the same, you can't simplify it (or its already simplified)

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

`(y^5)/(y^7)=y^(5-7)=y^(-2) = (1)/(y^2)` (when an exponent is negative, you move it to the other side of the fraction to make the exponent positive)

`(2x)/(3x^3) =?`

`(2x)/(3x^3)= ((2)/(3))x^(1-3)= ((2)/(3))x^(-2) = ((2)/(3))(1)/(x^2)` Since you can't simplify 2/3, you get:

(not sure if this is how it should look ---> (2/3)x^(1-3) but i'm assuming it is)

`(2)/(3x^2)`