The composition f(g(x)) is found by replacing the x in f(x) with the function g(x). So you'll have
f(g(x)) = -3(-6x-3) - 5 = 18x +9 -5 = 18x +4.
The domain of f is the same as the domain of g --- it's all real numbers. The composition is the equation of a line, and its domain is also all real numbers.
All u do is take -3x-5(-6x-3) applying the F.O.I.L. method ( Front Outer Inner Last). So Front = -3x times -6x=18x^2 Outer = -3x times -3=9x
Inner= -5 times -6x=30x Last = -5 times -3=15
So now u have 18x^2 + 9x + 30x + 15 combine like terms and you get 18x^2 + 39x + 15, but you are not done because you can simplify the equation by 3. So now you have 6x^2 + 13x + 5. Then for the domain since there is no limits or bounds it is all real numbers.
Hope this helped :)
P.S. Bannana this is a multiplying of functions and not a compostion of functions
Answers & Comments
Verified answer
The composition f(g(x)) is found by replacing the x in f(x) with the function g(x). So you'll have
f(g(x)) = -3(-6x-3) - 5 = 18x +9 -5 = 18x +4.
The domain of f is the same as the domain of g --- it's all real numbers. The composition is the equation of a line, and its domain is also all real numbers.
All u do is take -3x-5(-6x-3) applying the F.O.I.L. method ( Front Outer Inner Last). So Front = -3x times -6x=18x^2 Outer = -3x times -3=9x
Inner= -5 times -6x=30x Last = -5 times -3=15
So now u have 18x^2 + 9x + 30x + 15 combine like terms and you get 18x^2 + 39x + 15, but you are not done because you can simplify the equation by 3. So now you have 6x^2 + 13x + 5. Then for the domain since there is no limits or bounds it is all real numbers.
Hope this helped :)
P.S. Bannana this is a multiplying of functions and not a compostion of functions