Answer:
See below
Step-by-step explanation:
a. here you are to multiply the two functions together:
[tex](3x-1)(2x^{2} )=6x^{3}-2x^{2}[/tex]
b. here you are to subtract g from f:
[tex](3x-1)-(2x^{2})=-2x^{2}+3x-1[/tex]
c. here you are to compose g into f. In other words, pick up the whole g function and plug it into f wherever you see an x:
[tex]3(2x^{2} )-1=6x^{2} -1[/tex]
d. here you are compose f into g. In other words, pick up the whole f function and plug it into g wherever you see an x:
[tex]2(3x-1)^2[/tex]
You now have to FOIL out the (3x-1) like so:
[tex]2[(3x-1)(3x-1)][/tex]
which gives you
[tex]2(9x^{2} -6x+1)[/tex]
Distribute in the 2 and you'll end up with the answer:
[tex]18x^{2} -12x+2[/tex]
