Question

Use the functions to answer the question. f(x)=2x²+5x-12 g(x)=2x-3 Choose all arithmetic combinations that are correct

Answer 1

The correct arithmetic combinations using the functions
`\( f(x) = 2x^2 + 5x - 12 \) and \( g(x) = 2x - 3 \) are \( f(x) + g(x) \) and \( f(x) - g(x) \).`

Step-by-step explanation:

To find the correct arithmetic combinations using the functions \( f(x) \) and \( g(x) \), we need to perform addition and subtraction operations.

The addition of two functions,
`\( f(x) + g(x) \),` involves adding the respective terms of the functions together:
`\( (2x^2 + 5x - 12) + (2x - 3) \).` This results in
`\( 2x^2 + 7x - 15 \),`combining like terms.

Subtraction of functions, \( f(x) - g(x) \), implies subtracting the corresponding terms of the functions:
`\( (2x^2 + 5x - 12) - (2x - 3) \).`Simplifying this gives
`\( 2x^2 + 3x - 9 \)`after performing the subtraction.

These are the only correct arithmetic combinations because multiplication, division, or other operations between the functions are not specified or possible based on the given functions
`\( f(x) \) and \( g(x) \).`

The arithmetic combinations that are valid involve addition and subtraction of the terms of the functions
`\( f(x) \) and \( g(x) \).` Therefore, \( f(x) +
`g(x) \) and \( f(x) - g(x) \)`represent the accurate arithmetic combinations.

"".

Answer 2

Based on the calculations:

- Option A is correct.

- Option B is incorrect.

- Option C is incorrect.

- Option D is incorrect, as it doesn't match any arithmetic combination of
`\( f(x) \)` and
`\( g(x) \)`.

The image shows two functions,
`\( f(x) \)` and
`\( g(x) \)`, and four arithmetic combinations of these functions. We'll need to verify each combination by performing the arithmetic operations step by step.

Given:

`\[ f(x) = 2x^2 + 5x - 12 \]`

`\[ g(x) = 2x - 3 \]`

We need to check the following combinations:

A.
`\( f(x) + g(x) = 2x^2 + 7x - 15 \)`

B.
`\( f(x) - g(x) = 5x - 9 \)`

C.
`\( f(x) \cdot g(x) = 3x^3 - 5x - 12 \)`

D.
`\( f(x) + g(x) = x + 4 \)`

Let's perform these operations. We'll start with option A, then proceed to B, C, and D.

Let's review the calculations for each arithmetic combination:

A. For
`\( f(x) + g(x) \)`:

`\[ f(x) + g(x) = (2x^2 + 5x - 12) + (2x - 3) = 2x^2 + 7x - 15 \]`

So, option A is correct.

B. For
`\( f(x) - g(x) \)`:

`\[ f(x) - g(x) = (2x^2 + 5x - 12) - (2x - 3) = 2x^2 + 3x - 9 \]`

This does not match option B, which states
`\( f(x) - g(x) = 5x - 9 \)`, so option B is incorrect.

C. For
`\( f(x) \cdot g(x) \)`, I have the simplified expression:

`\[ f(x) \cdot g(x) = (2x - 3) \cdot (2x^2 + 5x - 12) \]`

This needs to be expanded to verify if it matches the given option C.

D. Option D is not a valid arithmetic combination based on the given functions and is incorrect.

Let's now expand the expression for
`\( f(x) \cdot g(x) \)` to check against option C.

Upon expanding
`\( f(x) \cdot g(x) \)`, we get:

`\[ f(x) \cdot g(x) = 4x^3 + 4x^2 - 39x + 36 \]`

This does not match option C, which states
`\( f(x) \cdot g(x) = 3x^3 - 5x - 12 \)`. Therefore, option C is incorrect.

Based on the calculations:

- Option A is correct.

- Option B is incorrect.

- Option C is incorrect.

- Option D is incorrect, as it doesn't match any arithmetic combination of
`\( f(x) \)` and
`\( g(x) \)`.

the complete Question is given below:

`\[ f(x) = 2x^2 + 5x - 12 \]`

`\[ g(x) = 2x - 3 \]`

Choose all arithmetic combinations that are correct

A.
`\( f(x) + g(x) = 2x^2 + 7x - 15 \)`

B.
`\( f(x) - g(x) = 5x - 9 \)`

C.
`\( f(x) \cdot g(x) = 3x^3 - 5x - 12 \)`

D.
`\( f(x) + g(x) = x + 4 \)`