Respuesta :
Answer: The answer is (c) [tex]-20x^2+14x-12;\textup{ all real numbers.}[/tex]
Step-by-step explanation: Given that there are two functions f and g, defined by
[tex]f(x)=-4x-2,\\\\g(x)=5x-6.[/tex]
We are to find f*g and also its domain.
[tex](f*g)(x)\\\\=f(x)g(x)\\\\=(-4x-2)(5x-6)\\\\=-20x^2+24x-10x-12\\\\--20x^2+14x-12.[/tex]
Also, its domain will be all real numbers, since the function f*g is defined at all 'x' in real numbers.
Thus, the correct option is
[tex]-20x^2+14x-12.[/tex]
Answer:
Option 3. (-20x2 + 14x + 12; domain: all real numbers) is the right answer.
Step-by-step explanation:
Let f(x) = -4x - 2 and g(x) = 5x - 6
then f(x)×g(x) = (-4x-2)(5x-6)
= -(4x+2)(5x-6)
= -( 20x²-24x+10x-12)
= -( 20x²-14x-12)
f(x)×g(x) = -20x² + 14x + 12
Since we know domain: f(x) ∈ R
Similarly for g(x) domain: g(x) ∈ R
Then domain of multiplication of both the function will be domain: f(x)×g(x) ∈ R.
