Question

F(x) = 8x2 – 2x + 3

g(x) = 12x2 + 4x – 3

What is h(x) = f(x) – g(x)?

Options:
h(x) = 20x2 + 2x
h(x) = –4x2 – 6x
h(x) = –4x2 – 6x + 6
h(x) = –4x2 + 2x

Answer 1

Answer:
`\text{h(x)}=-4x^2-6x+6`

Explanation:

Given functions :
`\text{f(x) }= 8x^2 - 2x + 3` (1)

`\text{g(x)} = 12x^2 + 4x - 3` (2)

To find :
`\text{ h(x) = f(x) - g(x)}`

Consider :
`\text{ h(x) = f(x) - g(x)}`

i.e. Subtract the expression for g(x) in equation (2) from the expression for f(x) in (1), we get

`\text{ h(x)}=8x^2 - 2x + 3-(12x^2 + 4x -3)`

Multiply (-) sign inside the parentheses, we get

`\text{ h(x) }=8x^2 - 2x + 3-12x^2 -4x +3`

Combine like terms, we get

`\text{ h(x) }=8x^2-12x^2 - 2x -4x + 3 +3\\\\\Rightarrow\text{h(x)}=-4x^2-6x+6`

Hence, the correct answer is
`\text{h(x)}=-4x^2-6x+6`

Answer 2

Correct option is (C).

Explanation:

`f(x) = 8 {x}^(2) - 2x + 3`

`g(x) = 12 {x}^(2) + 4x - 3`

Now,

h (x) =f (x) - g (x)

`h(x) = \: 8 {x}^(2) - 2x + 3 - 12 {x}^(2) - 4x + 3`

`h(x) = - 4 {x}^(2) - 6x + 6`

So, correct option is (C).

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