Answer: Choice A) 12x^2 - 48x + 21; all real numbers
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Work Shown:
(f * g)(x) = f(x) * g(x)
(f * g)(x) = ( f(x) ) * ( g(x) )
(f * g)(x) = ( -2x+7 ) * ( -6x+3 )
(f * g)(x) = -2x*( -6x+3 ) + 7*( -6x+3 )
(f * g)(x) = -2x*(-6x) - 2x*(3) + 7*(-6x) + 7*(3)
(f * g)(x) = 12x^2 - 6x - 42x + 21
(f * g)(x) = 12x^2 - 48x + 21
The domain is the set of all real numbers because we can plug in any number in for x, to get some output for y. There are no issues to worry about such as division by zero errors, square root of a negative number, etc.