Given f(x) = 2x - 1 and g(x) = 4x + 6,
which operation completes the statement?

f(x) ___ g(x) = 8x^2 + 8x - 6

i need to determine what math sign i have to use on the the options are *,+,-, and the divide symbol

this is operations on functions!!!

f(x) times g(x) = 8x^2+8x-6

(2x-1) times (4x+6) = 8x^2+8x-6

Explanation:

The functions f(x) and g(x) are linear functions. The result of f(x) ___ g(x) is some quadratic function.

It's very likely that the answer is a multiplication sign because of the general template of

(linear)*(linear) = (quadratic)

For example, x*3x = 3x^2.

Let's see if the two functions multiply out to 8x^2+8x-6 or not.

f(x) * g(x) = ( f(x) ) * ( g(x) )

f(x) * g(x) = ( 2x-1 ) * ( 4x+6 )

f(x) * g(x) = y * ( 4x+6 ) let y = 2x-1

f(x) * g(x) = 4xy + 6y   distribute

f(x) * g(x) = 4x( y ) + 6( y )

f(x) * g(x) = 4x( 2x-1 ) + 6( 2x-1 ) replace y with 2x-1

f(x) * g(x) = 8x^2-4x  + 12x-6   distribute twice more

f(x) * g(x) = 8x^2+8x-6

We end up getting the correct result. So this confirms that a multiplication sign is needed to fill in the blank.