Question

PLEASE HELP! LAST QUESTION (:

Consider the following:
f(x) = sqrt x
g(x)= x-5

Find each of the following functions and determine the domain of each:

f+g = sqrt x + x - 5 domain = ?
f-g= sqrt x - x +5 domain = ?
f x g = ? domain = ?
f/g = ? domain = ?

Answer 1

Okay, to start with, \[f*g = \sqrt(x)*(x-5) = x \sqrt(x) + 5 \sqrt(x)\] and\[f/g = \sqrt(x) / (x-5)\]

Since the square root isn't defined over the real numbers for negative x values, we see that the domains of the first 3 functions are all \[R^+ + {0}\] (that is, 0 plus all positive real numbers).

The fourth function will have the domain \[R^+ + {0} - {5}\] , since the function has x-5 in the denominator and division by 0 is undefined.

Answer 2

(By the way, the equation editor removed the brackets but that should be (R^+) + {0} and (R^+) + {0} - {5}

Answer 3

okay, im confused about the domain. because on my hw it says select all that apply and the choices are : all real numbers, x>0, x> or =0, x does not equal 0, x < or =0, x>5, x > or = 5, x does not equal 0, x < or = 5..

so what would it be according to that?

Answer 4

and also, my homework is saying that the answer to fxg is incorrect?

Answer 5

Okay, the first 3 should all be x >= 0. The last one should be x >= 0, x not = 5.

Answer 6

Oh, im sorry, i mistyped it - its \[x \sqrt(x) - 5 \sqrt(x)\] (I wrote + by mistake)

Answer 7

oh okay! thank you!

Answer 8

No problem! Post if you have any other questions, I'll keep an eye on the thread.

Answer 9

that was actually the last question (: but i just started this new class so ill prob be on here alot seeking help for the rest of the semester . thanks for all your help and hopefully i can learn more from you in the future

Answer 10

Any time. I'm fairly new to the site but I'm on a fair bit. Hopefully I'll see you around =D