## monroe17 3 years ago Find the domain and range of: f(x)=18sqrt(x)-17

1. TheMind

D={x: where x belong to R and x >=17} R={ y>=0}

2. monroe17

so, would it be 18x-17>=0? and solve?

3. dpaInc

is this your function: $$\large f(x)=18\sqrt{x}-17$$

4. monroe17

yes

5. monroe17

|dw:1346012919057:dw|

6. dpaInc

the domain of f is all the x values that give f(x) a real value.... so looking at the function, the function will not give you a real number when x is less than 0....

7. dpaInc

so the actual question in finding the domain is "what x values is $$\large \sqrt x =real$$ number

8. monroe17

would I do.. 18x-17<0 and solve?

9. love_math

x>=-17

10. love_math

root of x is always larger than 0

11. qpHalcy0n

You're just looking to be sure that what's under the root does not go negative. So x cannot be negative. Since the smallest value of x is 0 (because of the domain), then the range's minimum value will happen when x is 0. (So plug in 0 for x, and see what y is). The upper limit of the function will go on forever.

12. monroe17

-17?

13. qpHalcy0n

You got it, that's the minimum of the range. As x gets bigger and bigger, there is no limit, it just grows and grows forever.

14. monroe17

so.. [-17,infinity) ?

15. qpHalcy0n

That is your range, yes.

16. monroe17

how do I find the domain with this function?

17. monroe17

(-inf,inf) ?

18. qpHalcy0n

Well, as we talked about earlier, the domain would be anything that is a "no no". You have a square root, and here, you cannot take the square root of a negative number, as it has no real solutions.

19. qpHalcy0n

anything that is NOT a "no-no", sorry ;]

20. monroe17

1?

21. qpHalcy0n

No, you simply have sqrt(x), since you cannot take the square root of a negative number, we know that x MUST be greater than or equal to 0.

22. monroe17

so.. 17?

23. qpHalcy0n

|dw:1346014535907:dw|

24. qpHalcy0n

We're looking for x's that might make the equation undefined. That's what it means to find the domain. The only thing in this equation that can become undefined (or have no real solutions) is the square root. Which can't be negative.

25. monroe17

so x is all real numbers that are positive then?

26. qpHalcy0n

Yep, or in other words x >= 0

27. monroe17

how do I put that into interval notation though? [0,inf)