Question

Which expression is equal to (f - g)(x)?

Answer 1

The correct option is c.

`$7 x^2+2 x+13$` is equal to
`$(f-g)(x)$`.

To find the expression for
`\((f-g)(x)\)`, we need to subtract the function
`\(g(x)\)` from
`\(f(x)\)`. Let's do this step by step.

The functions
`\(f(x)\)` and
`\(g(x)\)` are given as:

`\[ f(x) = 7x^2 + 4 \]`

`\[ g(x) = 2x + 9 \]`

Now,
`\((f-g)(x)\)` is defined as:

`\[ (f-g)(x) = f(x) - g(x) \]`

Substituting the given functions into this, we get:

`\[ (f-g)(x) = (7x^2 + 4) - (2x + 9) \]`

Now, let's simplify this expression:

`\[ (f-g)(x) = 7x^2 + 4 - 2x - 9 \]`

To simplify the expression
`\((f-g)(x) = 7x^2 + 4 - 2x - 9\)`, you can simply subtract
`\(g(x)\)` from
`\(f(x)\)`:

`\[(f-g)(x) = f(x) - g(x) = (7x^2 + 4) - (-2x - 9)\]`

Now, you can simplify further by distributing the negative sign on
`\(-(-2x - 9)\)` to make it positive:

`\[(f-g)(x) = 7x^2 + 4 + (2x + 9)\]`

Now, combine like terms:

`\[(f-g)(x) = 7x^2 + 2x + 13\]`

So,
`\((f-g)(x) = 7x^2 + 2x + 13\)`.

Therefore, the answer is
`$7 x^2+2 x+13$`.

Answer 2

Answer: Option D

`(f-g)(x) = 7x^2 -2x -5`

Explanation:

We have two functions:

`f (x) = 7x ^ 2 +4\\\\g (x) = 2x + 9`

We must find (f-g)(x)

Then we must subtract the function f and the function g.

Therefore we have that:

`(f-g) (x) = f (x) -g (x)\\\\(f-g) (x) = 7x ^ 2 +4 - (2x + 9)\\\\(f-g) (x) = 7x ^ 2 -2x -5`

Therefore the correct option is the last option (Option D)
`(f-g)(x) = 7x^2 -2x -5`