Question

Pre-calculus Help!!!!! plz.....

Answer 1

\[f(x) = x \sqrt{25-x^2}\]

Answer 2

What is the question?

Answer 3

Find the domain..

Answer 4

what values of x would cause us to have a negative number underneath the square root?

Answer 5

the negative??

Answer 6

I'm not sure what you mean. Notice if x > 5 or x < -5, then we would have a negative number underneath the square root. Plug in 6, for example, then wewould get 25 - 36, which is -11.

Answer 7

uu...what??? This stuff is new to me.....

Answer 8

hmmm. Basically, we can't have any negative numbers underneath the square root.

Answer 9

The domain of a function are all values x that have a corresponding function value, which we call f(x). In essence, any number which you plug in for x that would cause the value underneath the square root symbol to be negative, would not be in the domain.

Answer 10

Ok. SO what would my answer be?? 5?

Answer 11

@mathmale

Answer 12

Hello, Yana!
The "domain" of a function is the set of all PERMITTED input values of the function. This implies that sometimes some inputs are permitted whereas others are not.

Take the function \[y=\sqrt{x}\] as an example. The only acceptable inputs (x-values) for this function are those that are zero or greater: \[[0,\inf)\]

Answer 13

Thus, if you're dealing with the function\[f(x) = x \sqrt{25-x^2}\]your job is to identify permitted x values.

RBauer4 was on target when he/she asked you, "what values of x would cause us to have a negative number underneath the square root?"

That's because \[25-x^2\] MUST be equal to or greater than zero.

Can you solve the inequality \[25-x^2\ge0?\] the solution set is the DOMAIN of the function given in your math problem posting.

Answer 14

Thanx for the information and helping me with this problem! I appreciate your help and your clear explanations. If you don't mind what do I do after i get
\[x^2\ge -25\]
Would it be -5??

Answer 15

@mathmale Can you finish?

Answer 16

\[If:~25-x^2\ge0,\] add (x^2) to both sides of this inequality. Then \[25 \ge x^2,~ or\]\[x^2 \le 25\]

You must find the set of numbers that satisfies this inequality.

It will look like [a, b], where a is the smallest x value that will satisfy the inequality and b is the largest.

That interval is the DOMAIN you want.

Answer 17

Sorry, Yana, but I have to get off the 'Net. Perhaps we could continue later if need be. :)

Answer 18

uuuuuggg.....Ok. It's fine..Somehow we'll figure it out.

Answer 19

Would it be...
[-5,5]??

Answer 20

Suggestions:

1) Replace the inequality sign with =: x^2 = 25. Solve this for x. One root will be +, the other -.

2) Draw a number line and mark those two roots: