## horsegirl27 one year ago Please help me out!! I have work for the first part of this question, but then I'm confused. When reading it, it seems like parts 2 and 3 are the same, so I would like some clarification of what to do. For part 4, I'm not quite sure either.... Question posted below.

1. horsegirl27

Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses. f(x)= x+a b g(x)=cx−d Part 2. Show your work to prove that the inverse of f(x) is g(x). Part 3. Show your work to evaluate g(f(x)). Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include 5 values for each function. Graph the line y = x on the same graph.

2. horsegirl27

I'm sorry, those functions are messed up, let me fix that.

3. horsegirl27

f(x)=x+a/b g(x)=cx-d

4. horsegirl27

So, for part 1, I have f(x)=x+3/5 and g(x)=5x-3. I'm not sure of what I'm doing in parts 2 and 3.

5. phi

is f(x) $f(x) = \frac{x+a}{b}$?

6. horsegirl27

yes.

7. phi

so we could write $f(x) = \frac{1}{b} x + \frac{a}{b}$

8. horsegirl27

For which part?

9. phi

just thinking out loud. For part 2, they want you to show the functions are inverses. start with your: f(x)=(x+3)/5 g(x)= 5x-3 if they are inverses then f( g(x) ) = x

10. phi

f( g(x) ) is short-hand for : everywhere you see "x" in the expression for f(x), erase the x and write g(x) using f(x)=(x+3)/5 g(x)= 5x-3 f( g(x) ) = ( g(x) +3 ) /5

11. horsegirl27

ok

12. phi

now we use g(x) = 5x-3 in f( g(x) ) = ( g(x) +3 ) /5 in other words, on the right hand side, replace g(x) with its "definition" 5x-3 can you do that ?

13. phi

you should get $f( g(x) ) = \frac{( 5x-3 +3)}{5}$

14. phi

now simplify that. For part 3, do almost the same thing show g( f(x) ) = x

15. horsegirl27

ok

16. horsegirl27

And I am so sorry, I was gone for a moment.

17. horsegirl27

Ok, so that's what I got for that part.

18. horsegirl27

So for part 3, to I basically just solve it to show g( f(x) ) = x?

19. horsegirl27

Because I worked it out and got it. Is that what I want to turn in for part 3, my work?

20. phi

I assume for part 2, you got f( g(x))= x after simplifying?

21. phi

$f( g(x) ) = \frac{( 5x-3 +3)}{5} = \frac{5x+0}{5} = \frac{5x}{5} = x$

22. horsegirl27

yes. That's my work exactly.

23. phi

for part 3 g( f(x) ) start with f(x)=(x+3)/5 g(x)= 5x-3 g(f(x)) means replace x in 5x-3 with f(x) what do you get ?

24. horsegirl27

g(f(x))=5(x+3/5)-3 Then the 3's will cancel each other out, and so will the 5's, to get g(f(x))=x.

25. phi

you have to remember order of operations. $g(f(x)) = 5 \cdot \frac{(x+3)}{5} -3$ multiply before add/subtract

26. horsegirl27

oh, sorry

27. horsegirl27

So then it will x+3/1 or 0? And then after that, the 3's will still cancel out, right?

28. phi

the 5/5 becomes 1 and you get $g(f(x)) = 5 \cdot \frac{(x+3)}{5} -3 \\ = 1\cdot (x+3) -3 \\=\ (x+3)-3 \\ =x+3-3 \\=x$

29. phi

just like $\frac{15}{5} = \frac{5 \cdot 3 }{5} = \frac{5}{5} \cdot 3 = 1 \cdot 3 = 3$

30. horsegirl27

ok, that makes sense.

31. horsegirl27

So for part 2, I'm showing for for f(x), and for part 3, showing work for g(x)? Then graphing? And I'm confused how I should graph this

32. phi

Include a table of values for each function. Include 5 values for each function. that means they want a table of x y values where y is f(x) or g(x) depending on which function you are doing.

33. horsegirl27

ok, so for x I could use something like 0, 1, 2, 3, -1 and for y -3, 2, 7, 12, -8? (i might not use those numbers, I just chose them randomly)

34. phi

Start with the first function f(x) f(x)=(x+3)/5 I would pick small negative and positive numbers for x to get integer answers for f(x) (i.e. y) for example if you start at x= -8, and make x go up by 5 , you will get nice numbers for f(x)

35. horsegirl27

ok, thanks.

36. horsegirl27

By the way, any suggestions for an online graph?

37. phi

38. horsegirl27

39. horsegirl27

So, graph 5 points for each?

40. phi

First write down the table x | f(x) -------- -8 | -1 -3 | 0 etc and for g(x) you can pick x= -2 to +2 by 1 x | g(x) -------- -2 | -13 -1 | -8 etc

41. phi

if you use geogebra you type in f(x)= (x+3)/5 and it will plot the line

42. horsegirl27

ok

43. horsegirl27

Got it, thanks!

44. horsegirl27

I have one more question, want me to make a new thread?

45. phi

Here is the plot

46. horsegirl27

thank you :D