Question

Let f(x) = -4x - 2 and g(x) = 5x - 6. Find f*g and state its domain.

8x2 + 34x - 30; all real numbers

8x2 + 34x - 30; all real numbers except x = 1

-20x2 + 14x + 12; all real numbers

-20x2 + 14x + 12; all real numbers except x = 6

Answer 1

Answer: The answer is (c)
`-20x^2+14x-12;\textup{ all real numbers.}`

Step-by-step explanation: Given that there are two functions f and g, defined by

`f(x)=-4x-2,\\\\g(x)=5x-6.`

We are to find f*g and also its domain.

`(f*g)(x)\\\\=f(x)g(x)\\\\=(-4x-2)(5x-6)\\\\=-20x^2+24x-10x-12\\\\--20x^2+14x-12.`

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

`-20x^2+14x-12.`

Answer 2

Option 3. (-20x2 + 14x + 12; domain: all real numbers) is the right answer.

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.