Question

Find (f+g)(x) and (f-g) (x) for the given functions f and g. f(x) = x +8, g(x) = x-8

Answer 1

I am trying to figure out this how set this up and solve

Answer 2

Whenever we operate functions, we treat them as numbers, to later on, as a univariable equality.
I'll do the sum, to show you an example:
if:
\[f:f(x)=x+8\]
\[g:g(x)=x-8\]
Then, the sum would be:
\[(f+g)(x)=f(x)+g(x)\]
but we already know the values of them, they were given there above, so let's replace it:
\[(f+g)(x)=(x+8)+(x-8)\]
Doing a little algebra, and getting rid of the parenthesis:
\[(f+g)(x)=x+8+x-8\]
\[(f+g)(x)=2x\]

Answer 3

It's the same with the sustraction, try it and let me know the result you got :)

Answer 4

Is the other one 8x

Answer 5

@Owlcoffee is this right

Answer 6

That's, incorrect, friend, can I see what you did?

Answer 7

I deleted what I did already

Answer 8

Well, don't worry, I'll give you a little step:
if:
\[f:f(x)=x+8\]
\[g:g(x)=x-8\]
Then:
\[(f-g)(x)=(x+8)-(x-8)\]
remember the distributive property, or when you sustracted polynomials earlier in basic algebra, so all we do is distribute that "-" and by the law of signs:
\[(f-g)(x)=x+8-x+8\]
I'll let you handle the rest.

Answer 9

is 16 the answer

Answer 10

that's correct.

Answer 11

Cool

Answer 12

Thanks for your help

Answer 13

Will it be 16x or just 16 @Owlcoffee

Answer 14

just 16, because the x's cancelled.
we call that a "constant function"

Answer 15

ok

Answer 16

Thanks for your help today