Danny L.

asked • 02/12/20

f+g, f-g, fg, f/g

f(x)= √(16-x2 )

g(x)= √(x2-9)


Need F+g

f-g

fg

f/g

And there domains. Thanks!

1 Expert Answer

By:

LEV K. answered • 02/12/20

Tutor
4.9 (101)

Mid and High School Math and SAT prep
About this tutor ›
About this tutor ›

1) For f+g just add two formulas

sqrt(16-x2) + sqrt(x2-9)

The domain is 16-x2>=0 and x2-9 >=0

That mean you should take the intersection

The answer is

[-4,-3] ∪ [3,4]


For all other functions compositions do similarly. The domain will be the same, except f/g - you can't divide by 0. So just additionally exclude points 3 and -3: [-4,-3) ∪ (3,4]

Upvote • 0 Downvote
More
Report

Danny L.

Would you break it down? Like sqrt((4-x)(x+4))+ sqrt((x+3)(x-3)) ?
Report

02/12/20

LEV K.

tutor
You could. Both inequalities will then be easily solved using interval method. Don't forget to take an intersection if these 2. Also, in f*g ans f/g - do not combine expressions under the single sqrt, altough it is tempting. That will expand the domain
Report

02/12/20

Danny L.

What do you mean do not combine expression? Keep it as sqrt 16-x^2/ sqrt x^2-9) ?
Report

02/12/20

LEV K.

tutor
Well, you are tempted to do f*g = sqrt ( (x2-9)*(16-x2) )
Report

02/12/20

LEV K.

tutor
Keep it as you suggested, 2 separate roots
Report

02/12/20

Danny L.

Oh, so keep it 3 seperae roots for f *g. What about f/g? would it be (sqrt of (16-x^2) * swrt(x^2-9))/ x^2-9
Report

02/12/20

LEV K.

tutor
for f/g you will get sqrt(16-x2) / sqrt(x2-9)
Report

02/12/20

Danny L.

I think I'm good. I think I'm just overthinking these problems. Thank you for your help
Report

02/12/20

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.