Question

find the domain of the given function f(x) = sqrt x + 3 / (x+ 8)(x-2)
A. x > 0
B. all real numbers
C. x>/= -3, x cannot = 2
D. x cannot = 8, x cannot = -3, x cannot = 2

Answer 1

\[f(x)=\sqrt{x}+\frac{3}{(x+8)(x-2)} ?\]

Answer 2

the sqrtx is in the denominator with the 3

Answer 3

it's in the denominator ?

Answer 4

i'm not sure how to interpret it then
the denominator is in bottom

Answer 5

sorry i meant numerator

Answer 6

the numerator is sqrt x + 3

Answer 7

\[f(x)=\frac{\sqrt{x}+3}{(x+8)(x-2)}\]

Answer 8

yes

Answer 9

first do you know the domain of the function g(x)=sqrt(x) ?

Answer 10

no

Answer 11

what happens when you have sqrt(negative number)?

Answer 12

i don't think you can do that

Answer 13

so you can only do square root of positive or zero numbers

(well over the real numbers anyways)

Answer 14

so the domain for g(x)=sqrt(x) is x is positive or zero
we say x is in [0,inf)
where inf means infinity

Answer 15

so now let's look at your denominator

Answer 16

we cannot divided by zero
what values of x will make the denominator 0?

Answer 17

-8 and +2

Answer 18

right so the domain of the function
\[f(x)=\frac{\sqrt{x}+3}{(x+8)(x-2)} \text{ is } \\ x \ge 0 \text{ but } x \neq -8 \text{ or } 2 \\ \text{ we don't even have \to mention } x \neq -8 \text{ since that is redundant } \\ \text{ so you can say instead } \\ x \ge 0 \text{ but } x \neq 2\]

Answer 19

are you sure the numerator wasn't suppose to be sqrt(x+3) ?

Answer 20

the sqrt sign is over the x and the 3

Answer 21

so it was suppose to be sqrt(x+3) and not sqrt(x)+3
\[f(x)=\frac{\sqrt{x+3}}{(x+8)(x-2)}\]

Answer 22

right

Answer 23

use what we said about square roots above
you need the inside to be positive or zero of the square root
so you need x+3 to need be positive or zero
in math symbols that looks like
\[x+3 \ge 0\]
solve this
and then you already pointed out that x cannot be -8 or 2

so anyways let me know what you get when you solve the above inequality

Answer 24

x is greater than or equal to -3

Answer 25

right now from that set we want to exclude -8 and 2
one of these values is already excluded from the set x> or =-3

Answer 26

so its d

Answer 27

?