Question

1. Consider the following functions. f(x) = 3x2 + x + 2 g(x) = 4x2 + 2(3x – 4) h(x) = 5(x2 - 1) a. Find f (x) - g(x). b. Find g(x) - h(x).

Answer 1

a.

Let's write function g(x) better:

`g(x)=4x^2+2(3x-4)=4x^2+6x-8`

Now we can do the substraction easier

`f(x)-g(x)=(3x^2+x+2)-(4x^2+6x-8)_{}`
`f(x)-g(x)=3x^2+x+2-4x^2-6x+8`
`f(x)-g(x)=(3-4)x^2+(1-6)x+2^{}+8`
`f\mleft(x\mright)-g\mleft(x\mright)=-x^2-5x+10`

That's answer a

b.

We write h(x) better too:

`h(x)=5(x^2-1)=5x^2-5`

And do the same as before:

`g(x)-h(x)=(4x^2+6x-8)-(5x^2-5)`
`g(x)-h(x)=4x^2+6x-8-5x^2+5`
`g(x)-h(x)=(4-5)x^2+6x-8+5`
`g(x)-h(x)=-x^2+6x-3`

That's answer b