Question

if f(x)=3x-7 and g(x)=x^3-3x-x+1 find the following: a) f(-2) + [g(4)]^2 b) (f*g)(x) c) f[g(x)] d) g [f(x)]

Answer 1

answers or process?

Answer 2

and are you sure g(x)=x^3-3x-x+1
or should it be g(x)=x^3-3x^2-x+1

Answer 3

no mistake g(x)=x^3-2x^2-x+1

Answer 4

a)
\[f(-2)=3(-2)-7=-13\]\[g(4)=4^3-3(4)^2-4+1=13\]\[[g(4)]^2=13^2=169\]so \[f(-2) + [g(4)]^2= ???????\]
b) I assume this is f(x)*g(x), so
\[f(x)=3x-7\]\[g(x)=x^3-3x^2-x+1\]\[f(x)*g(x)=(3x-7)(x^3-3x^2-x+1)\] you should be able to multiply this out yourself, then simplify if needed.

c)\[f[g(x)]=3(x^3-3x^2-x+1)-7=3x^3-9x^2-3x-4\]
notice how the expression for g(x) was just inserted into where the x goes in the expression for f(x), then we simplified. Using this idea you shoud be able to do part d) yourself.
Good luck, let me know if you have any troubles, and if so, where.

Answer 5

is the answer to d 6x^3+11x^2-4

Answer 6

that can't be right because just looking at the x^3 term it should be 27x^3, so I will set the problem up for you:\[g[f(x)]=(3x-7)^3-3(3x-7)^2-(3x-7)+1\]the algebra here is tedious but \[(3x-7)^3=27x^3-189x^2+441x-343\]and \[(3x-7)^2=9x^2-42x+49\]
so now we have\[ [g[f(x)]=27x^3-189x^2+441x-343-3(9x^2-42x+49)-(3x-7)+1\]simplify this and see what you get.

Answer 7

sorry, last line is [g(f(x)]=
\[27x^3−189x^2+441x−343−3(9x^2−42x+49)−(3x−7)+1\]

Answer 8

is this so far right 27x^3 -162x^2+567x+147

Answer 9

I see where you made at least one mistake: you made the x^2 term
\[-189x^2-3(9x^2)=-189x^2-27x^2=-216x^2\]watch the minus signs, you are clearly having trouble with the algebra here, so try to take it step by step
The answer you should get is\[g[f(x)]=27x^3-216x^2+564x-482\] You should keep trying until you get this result on your own, and try to see where you made mistakes.