## anonymous one year ago 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)

1. freckles

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

2. freckles

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

3. freckles

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

4. anonymous

ok i have a question

5. anonymous

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

6. anonymous

im lost

7. freckles

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

8. anonymous

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

9. anonymous

whats going on?

10. freckles

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

11. anonymous

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

12. anonymous

freckles, yes.

13. anonymous

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

14. freckles

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

15. anonymous

okay

16. freckles

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

17. anonymous

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

18. 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) ?

19. anonymous

no

20. 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

21. anonymous

no i wasn't.

22. freckles

try this one: $(f-g)(x)=f(x)-g(x)$

23. anonymous

no clue

24. 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)

25. anonymous

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

26. anonymous

i understand none of this and it gets frustrating

27. 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

28. anonymous

I'm attempting to follow

29. 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

30. 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

31. anonymous

ok

32. freckles

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

33. freckles

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

34. freckles

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