Question

Let / f(x)= -5x + 3 and g(x) = 6x - 2. Find f*g and its domain.

Answer 1

Answer:

The correct answer is:  Option 3.

Step-by-step explanation:

To begin the problem asks to find $f$· $g$ which can be defined as $[f*g](x)$. Now we are given that:

$f(x)=-5x+3\\g(x)=6x-2$

So now we need to 'multiply' our two algebraic expressions as follow:

$fg(x)=(-5x+3)(6x-2)\\fg(x)=(-5x)(6x) +(-2)(-5x)+(3)(6x)+(3)(-2)\\fg(x)=-30x^2+10x+18x-6\\fg(x)=-30x^2+28x-6$ Eqn.(1)

The domain of Eqn. (1) is all real numbers of $x$.

Which according to the given options , Option 3 is correct.