Question

F(x) = 3x-1 and g(x)=2x^2

a. Find (f g) (x).


b. Find (f-g) (x).


c. Find f(g(x)).


d. Find g(f(x)).

Answer 1

See below

Explanation:

a. here you are to multiply the two functions together:

`(3x-1)(2x^(2) )=6x^(3)-2x^(2)`

b. here you are to subtract g from f:

`(3x-1)-(2x^(2))=-2x^(2)+3x-1`

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:

`3(2x^(2) )-1=6x^(2) -1`

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:

`2(3x-1)^2`

You now have to FOIL out the (3x-1) like so:

`2[(3x-1)(3x-1)]`

which gives you

`2(9x^(2) -6x+1)`

Distribute in the 2 and you'll end up with the answer:

`18x^(2) -12x+2`