Question

If f(x) = 6x - 4 and g(x) = 2x^3, find g(3) - f(4)

Answer 1

Evaluating g(3) and f(4) with their respective function definitions, g(3) = 54 and f(4) = 20. Subtracting these gives g(3) - f(4) = 34, which is the final answer.

Step-by-step explanation:

To find g(3) - f(4), we need to evaluate each function separately with the given inputs and then find the difference between the two results.

First, let's evaluate g(3):

• g(x) = 2x^3
• g(3) = 2(3)^3
• g(3) = 2(27)
• g(3) = 54

Now, let's evaluate f(4):

• f(x) = 6x - 4
• f(4) = 6(4) - 4
• f(4) = 24 - 4
• f(4) = 20

Finally, we subtract f(4) from g(3):

• g(3) - f(4) = 54 - 20
• g(3) - f(4) = 34

The result of g(3) - f(4) is 34.

Answer 2

To solve the problem, simply plug in the value for x in both functions, as shown below:

`f(4) = 6(4) - 4`

-->
`f(3) = 24 - 4`

--->
`f(3) = 20`

`g(3) = 2(3)^3`

-->
`g(3) = 2 * (3^3)`

--->
`g(3) = 2 * 27`

---->
`g(3) = 54`

`g(3) - f(4) = 54 - 20`, so the answer is 34.