Respuesta :

[tex]f(x) + g(x) = 3x + 2 + x + 6 = 4x + 8[/tex].  This function is defined for all real numbers.

[tex]f(x) - g(x) = (3x + 2) - (x + 6) = 2x - 4[/tex].  This function is also defined for all real numbers.

[tex]f(x) \cdot g(x) = (3x + 2) \cdot (x + 6) = 3x^2 + 2x + 18x + 12 = 3x^2 + 20x + 12.[/tex]  As before, this function is defined for all real numbers [tex]x[/tex].

[tex]\frac{f(x)}{g(x)} = \frac{3x+2}{x+6}[/tex].  Fractions are undefined when their denominators are zero, so if [tex]x + 6 = 0[/tex], this function is undefined.  Thus, the domain is all real numbers except [tex]x = -6[/tex].
I'll do f+g, you try the others on your own and comment if you need help with them! For f+g, you're just going to add the two functions together:

[tex]f (x) = 3x + 7 [/tex]

[tex]g (x) = x + 9[/tex]

[tex](f +g)(x) = (3x + 7) + (x + 9) = 4x + 16[/tex]

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