Let f(x) = 3x + 2 and g(x) =7x + 6. Find f ·g and its domain. A. 6x2 + 4x + 42; all real numbers except x = ­2/3 B. 21x2 +32x + 12; all real numbers except x = -6/7 C. 6x2 + 4x + 42; all real numbers D. 21x2 + 32x + 12; all real numbers

Answer:The answer is the option D[tex]21x^{2}+32x+12[/tex] ; All real numbersStep-by-step explanation:we have[tex]f(x) = 3x + 2[/tex][tex]g(x) =7x + 6[/tex]Calculate f(x)*g(x)[tex](3x + 2)*(7x+6)[/tex]Multiply applying the distributive property[tex](3x + 2)*(7x+6)=3x*7x+3x*6+2*7x+2*6\\=21x^{2}+18x+14x+12\\=21x^{2}+32x+12[/tex]The domain of the function is the interval------> (-∞,∞)All real numbers