## anonymous one year ago if f(x) = x^2 -3x and g(x) = (√x)-1, then f(g(x)) =

1. Nnesha

f(g(x)) can be written as f(sqrt{x}-1) so replace x with g(x) function into f(x) equation

2. anonymous

i did but i still dont get it unfortunatey

3. Nnesha

$\huge\rm f(x)=x^2-3x$ replace x with sqrt{X} -1

4. Nnesha

what did you get ? can i see ur work plz

5. anonymous

i got ((√x)-1)^2 - 3((√)-1)

6. Nnesha

$\huge\rm (\sqrt{x}-1)^2-3(\sqrt{x}-1)$ distribute 2nd parentheses by -3 and apply foil method for (sqrt{x}-1)^2

7. Nnesha

do you know how to distribute ?-3(Sqrt{X}-1) ?

8. anonymous

no i dont unfortunately. I dont know how to distribute the -3 to the sqaure roots or how to do the first set of parenthesis

9. Nnesha

apply distributive property distribute parentheses by outside number/ $\huge\rm \color{reD}{a}(b+c) =\color{red}{a} ·b +\color{reD}{a}·c =\color{ReD}{a}b +\color{ReD}{a}c$

10. Nnesha

$-3(\sqrt{x}-1)$ multiply -3 times sqrt{x} and then -3 times -1

11. anonymous

oh okay. I got this for the second set of parenthesis: -3√x+3

12. anonymous

how do i foil square roots?

13. Nnesha

yes right now foil (sqrt{x} -1)^2 is same as $\huge\rm (\sqrt{x}-1)(\sqrt{x}-1)$|dw:1442527466021:dw| multiply 2nd parentheses by by first term sqrt{x} and then by -1

14. anonymous

i ended up getting : √2x -√x -√x +1

15. anonymous

i mean: √x^2 - √2x +1

16. Nnesha

$\sqrt{2x}$isn't right

17. Nnesha

|dw:1442528022410:dw| it would -2sqrt{x}

18. Nnesha

just like variables when we combine them we should coefficient add/subtract their coefficient

19. anonymous

so it isnt √x^2 - √2x +1 ?

20. Nnesha

just like variables when we combine them we should coefficient add/subtract their coefficient so $-\sqrt{x}-\sqrt{x}=-2\sqrt{x}$

21. anonymous

for the first set of parenthesis

22. Nnesha

2nd term isn't right

23. anonymous

oh okay i see. so is it: √x^2 - 2√x +1

24. Nnesha

yes right now square root can cancel out the square so sqrt{x^2} = ??

25. anonymous

okay so it would be x - √2x +1 -3√x +3???

26. Nnesha

yes right $\huge\rm x-2\sqrt{x}+1-3\sqrt{x}+3$ now combine like terms

27. anonymous

so it would be x-5√x+4?

28. Nnesha

yes looks right!

29. anonymous

thank you very much for your help :)

30. Nnesha

yw :=)

31. Nnesha

did a great job!