Combining Functions and Finding their Domains

[Zaraydis]

Hi, I have a question about this problem:

Find f + g, f − g, fg, and f/g and their domains.

f(x) =

9 − x2

, g(x) =

1 + x

*(The square root symbol is over the whole answers excluding where a +,-, or / divides the equation)(As well as the functions above)
(f + g)(x) =√9-x^2 + √1+x
(f − g)(x) =√9-x^2 - √1+x
(fg)(x) =√9+9x-x^3-x^2
(f/g)(x) =(√9-x^2) / (√1+x)

That is the work I have done, and I am certain all of the answers are correct for combining the functions. However where I am stuck is at finding each of their domains. I am completely lost. I know for example with (f+g)(x) you would take 9-x^2 and 1+x and solve for x. I believe you would also turn this into a inequality but I am unsure of how to figure out which way the inequality symbol faces and whether or not it includes the (or equal to) as well. After it's in an inequality, I know how to graph them and test it to see if the numbers are included or not. My problem I believe is my algebra skills and not knowing how to turn this into an inequality to find the domain.

If someone could help explain how to do this, that would be great. Thank you so much!

 

[Deleted member 4993]

Hi, I have a question about this problem:

Find f + g, f − g, fg, and f/g and their domains.

f(x) =

9 − x2

, g(x) =

1 + x

*(The square root symbol is over the whole answers excluding where a +,-, or / divides the equation)(As well as the functions above)
(f + g)(x) =√9-x^2 + √1+x
(f − g)(x) =√9-x^2 - √1+x
(fg)(x) =√9+9x-x^3-x^2
(f/g)(x) =(√9-x^2) / (√1+x)

That is the work I have done, and I am certain all of the answers are correct for combining the functions. However where I am stuck is at finding each of their domains. I am completely lost. I know for example with (f+g)(x) you would take 9-x^2 and 1+x and solve for x.

For domain restriction, in these functions, you need to find for which values of x the term (function) inside the square root remain positive.

for example

for the function f(x) the domain is restricted to abs(x) ≤ 3 or -3 ≤ x ≤ 3

for the function g(x) the domain is restricted to x ≥ (-1)

So when you consider the domain for f + g you'll need to consider the intersection of these two sets and that will be -1 ≤ x ≤ 3

now show how you would find the same for the rest of the functions.

I believe you would also turn this into a inequality but I am unsure of how to figure out which way the inequality symbol faces and whether or not it includes the (or equal to) as well. After it's in an inequality, I know how to graph them and test it to see if the numbers are included or not. My problem I believe is my algebra skills and not knowing how to turn this into an inequality to find the domain.

If someone could help explain how to do this, that would be great. Thank you so much!

.

 

[lookagain]

Hi, I have a question about this problem:

Find f + g, f − g, fg, and f/g and their domains.

f(x) =

9 − x2

, g(x) =

1 + x

*(The square root symbol is over the whole answers excluding where a +,-, or / divides the equation)(As well as the functions above)


(f + g)(x) = √(9 - x^2) + √(1 + x )

(f − g)(x) = √(9 - x^2) - √(1 + x)

(fg)(x) = √(9 + 9x - x^3 - x^2)

(f/g)(x) = (√(9 - x^2))/(√(1 + x))


- - - - - Or,

(f/g)(x) = √(9 - x^2)/√(1 + x) works as well.

Zaraydis,

you have to use grouping symbols. Because you are already
able to type out that square root sign, go ahead and put
parentheses around the expressions as done by me above.


Also, space out your symbols, please. It is difficult to
read your characters in your lines when they are so
compacted next to each other.