help please.
Find (f + g)(x), (f - g)(x), (f . g)(x), and (f/g)(x) for each f(x) and g(x).
1. f(x) = a^2 - 1 , g(x) = a/(a + 1)
(f+g)(x)
(f-g)(x)
and
(f/g)(x)

- anonymous

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- freckles

(f+g)(x) means to add f(x) and g(x)

- freckles

(f-g)(x) means to take away g(x) from f(x)
or just write f(x)-g(x)

- freckles

(f/g)(x) means to write f(x)/g(x)

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## More answers

- anonymous

ok i have a question

- anonymous

what is wrong with this picture \[f(x) = a^2 - 1\]

- anonymous

im lost

- freckles

it is a constant function satellite :p
example:
\[f(x)=2 \\ g(x)=3+x \\ \text{ then } (f+g)(x)=2+(3+x)=5+x \\ \text{ also } (f-g)(x)=2-(3+x)=-x-1 \\ \text{ and } (\frac{f}{g})(x)=\frac{2}{3+x}\]

- anonymous

me too
if you have a function of x, it should have an x in it

- anonymous

whats going on?

- freckles

well are your functions really f(x)=a^2-1 and g(x)=a/(a+1) ?

- anonymous

don't know
does it really say
\[f(x)=a^2-1\] or is it
\[f(x)=x^2-1\]

- anonymous

freckles, yes.

- anonymous

what it says is what it is. I'm just not understanding how to solve it.

- freckles

whatever they are
just add f(x) and g(x) to find (f+g)(x)

- anonymous

okay

- freckles

have you found (f+g)(x)?

- anonymous

nope I've been trying but i don't know what I'm doing

- freckles

do you know how to add f(x) and g(x)
that is do you know how to add a^2-1 and a/(a-1) ?

- anonymous

no

- freckles

\[(f+g)(x)=f(x)+g(x) \\ =a^2-1+\frac{a}{a-1}\]
that is it unless you are asked to combine the fractions

- anonymous

no i wasn't.

- freckles

try this one:
\[(f-g)(x)=f(x)-g(x)\]

- anonymous

no clue

- freckles

f(x)=a^2-1
and g(x)=a/(a-1)
all you have to do is replace f(x) with a^2-1
and g(x) with a/(a-1)

- anonymous

what exactly am i doing with this? and should the answer be a equation?

- anonymous

i understand none of this and it gets frustrating

- freckles

the expression should be an expression of x
in this case the expression of x is a constant expression since the expression is really an expression in terms of a

- anonymous

I'm attempting to follow

- freckles

pretend f(x)=5 and g(x)=6
(f+g)(x)=f(x)+g(x)=5+6=11
you are just replacing f(x) with 5 and g(x) with 6
(f-g)(x)=f(x)-g(x)=5-6=-1
I just replaced f(x) with 5 and g(x) with 6
(f/g)(x)=f(x)/g(x)=5/6
again I just replaced f(x) with 5 and g(x) with 6

- freckles

(f*g)(x)=f(x)*g(x)=5*6=30
again I just replaced f(x) with 5 since in my example I let f(x)=5
and I just replaced g(x) with 6 since in my example I let g(x)=6

- anonymous

ok

- freckles

ok now you try finding (f-g)(x) for your f(x) and g(x)

- freckles

remember (f-g)(x) is the same as f(x)-g(x)

- freckles

just replace f(x) with a^2-1
and g(x) with a/(a-1)

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