Question

How do I find functions of f(x) and g(x)?
I'm currently struggling to understand how to do these problems for my Algebra 2 class. If anyone would be willing to walk me through the steps and explain why/how I do them that would be great!

The functions f(x) and g(x) are shown below:
f(x)=x^2-7
g(x)=x^2+3x+7

Show the algebraic processes explaining the steps used to determine the simplified expressions containing these functions as specified below.
Part A: Find f(x)-g(x)
Part B:A function, h(x) exisys such that h(x)=f(x)*g(x), What is the equation that function h(x) represents?
Part C: Find f(x)

Answer 1

f(x)-g(x) means you subtract ALL of g(x) from f(x)

Answer 2

f(x)-g(x) = [ f(x) ] - [ g(x) ]

f(x)-g(x) = [ x^2-7 ] - [ x^2+3x+7 ]

f(x)-g(x) = x^2-7 - x^2-3x-7 ... distribute

f(x)-g(x) = -3x - 14 ... combine like terms

does that make sense?

Answer 3

Yes it does! Can you explain how do I find part b? I don't get how to find the function of h(x)

Answer 4

you will be multiplying f and g (instead of subtracting)

what do you get when you do so?

Answer 5

Would I get -3x *28?

Answer 6

you will have this as part of your steps

h(x) = f(x) * g(x)

h(x) = [ f(x) ] * [ g(x) ]

h(x) = [ x^2-7 ] * [ x^2+3x+7 ]

what comes next?

Answer 7

You would distribute, I got h(x)=x^4+3x^3-21x-49, is that right?

Answer 8

that is correct

Answer 9

"Part C: Find f(x)"

makes no sense to me because they already gave you f(x)

Answer 10

Oh I didn't finish typing part c, my bad! Part c: find f(x)+g(x)

Answer 11

so you just add the functions now

Answer 12

follow the same steps for subtracting, but replace the subtraction symbol with a plus symbol

Answer 13

Is the answer for part c 2x^2+3x ?

Answer 14

you nailed it

Answer 15

Thank you so much! (:

Answer 16

you're welcome