1. anonymous

2. ***[ISURU]***

do u know the meaning of using [ ] or () brackets ?

3. anonymous

Yes

4. ***[ISURU]***

well ... then ur 1st Question ask for a function ( which i will denote by f(x) ) which should be greater than or equal to 0 but lesser than + infinity ..... usually functions with square roots belongs to this type

5. ***[ISURU]***

$f(x) = \sqrt{x}$ this is a very simple example

6. ***[ISURU]***

u cant find the square root of $\sqrt{-3}$ or any other negative number.... got it ?

7. anonymous

Okay, got it.

8. ***[ISURU]***

the second one says... a function which is greater than - infinity and lesser than + infinity... usually ...almost any linear function satisfy this

9. ***[ISURU]***

$f(x) = x + 8$$f(x) = 5x + 10$....like any u like...

10. anonymous

Oh okay

11. ***[ISURU]***

these functions can take either negative or positive values... no harm happens :)

12. anonymous

Okay cool

13. ***[ISURU]***

now for the last one... its the same as the second one ..but it cant be equal to zero...usually a function with this range means that the function is a fraction ...like the below one

14. ***[ISURU]***

$f(x) = \frac{ 5x + 8 }{ x}$

15. ***[ISURU]***

if u substitute 0 in the above one...u wont be able to tell what will be the answer... because a number divide by zero could be either + infinity or - infinity

16. anonymous

Right, ok, got it.

17. anonymous

:)

18. ***[ISURU]***

soo... in a fraction the denominator cant be zero... any function with a fraction where the denominator will be 0 when x is 0 will be ur answer for the third and last of ur first question :)

19. ***[ISURU]***

now... do u want help in the 2nd one too ?

20. anonymous

Yes please. Thank you for helping me with the first question! :)

21. ***[ISURU]***

u r welcome :) lets c... the 2nd one

22. ***[ISURU]***

they say the original price is "x" and the price after you apply the coupon is f(x) ...... what happens when u applied the coupon is.... the cut off 25 dollars ..... so if the price of ur dress is "x" ...after u apply the coupon ..the price is " x -25 " ...because they cut off 25\$

23. ***[ISURU]***

so... f(X) = X -25 ...got it ?

24. anonymous

Okay I understand that

25. ***[ISURU]***

now lets consider g(x) ..... g(x) is the price of dress withe the 20% discount applied.... a 20% discount means that u can buy the dress less than 20% of the original price if the original price is "x" then 20% of "x" is (20/100)x then g(x) = x - (20/100)x got it ?

26. anonymous

Yes that makes sense

27. ***[ISURU]***

and finally .... ( f o g )(x) means f( g (x) )...where u have to substituent g(x) instead of "x" in f(x) therefor (f o g)(x) = g(x) - 25 = x - (20/100)x - 25

28. ***[ISURU]***

in the same way (g o f)(x) means g ( f(x) ) where u have to substitute "f(x)" instead of "x" in "g(x)" therefor (g o f)(x) = f(x) - (20/100)f(x) = x - 25 - [ (20/100)( x -25) ]

29. ***[ISURU]***

i hope u understand it :)

30. anonymous

Those two I was really confused on, but I understand them now :)

31. anonymous

Thank you sooo much!! I really appreciate it! :)

32. ***[ISURU]***

u r welcome :)