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anonymous

  • one year ago

A student says that the functions f(x) = 2x+2 and g(x) =2x-2 are inverse functions because their graphs are parallel. Is the student's reasoning correct? Justify your answer

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  1. anonymous
    • one year ago
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    @Nnesha

  2. anonymous
    • one year ago
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    Please help me @Nnesha

  3. anonymous
    • one year ago
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    @jim_thompson5910

  4. anonymous
    • one year ago
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    Someone please help me....

  5. jim_thompson5910
    • one year ago
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    what do you get if you solve y = 2x+2 for x?

  6. anonymous
    • one year ago
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    Umh, you would get y=x-2/2

  7. anonymous
    • one year ago
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    Right?

  8. anonymous
    • one year ago
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    And then the other one would be y=x+2/2

  9. jim_thompson5910
    • one year ago
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    yes \[\Large y = \frac{x-2}{2}\] that is equivalent to \[\Large y = \frac{1}{2}x - 1\] what is the slope of the second equation I wrote?

  10. anonymous
    • one year ago
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    1/2

  11. anonymous
    • one year ago
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    or would it be -1? Because I know that would be the y intercept right

  12. jim_thompson5910
    • one year ago
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    it's 1/2

  13. anonymous
    • one year ago
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    Ok

  14. jim_thompson5910
    • one year ago
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    so in y = 2x+2, the slope is 2 in y = (1/2)x - 1, the slope is 1/2

  15. jim_thompson5910
    • one year ago
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    the slopes are not equal, so the lines aren't parallel

  16. anonymous
    • one year ago
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    And that would mean that the two functions are not inverses, right?

  17. jim_thompson5910
    • one year ago
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    no when we solved for x and swapped x and y, we found the inverse

  18. anonymous
    • one year ago
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    But don't inverse functions have to equal x?

  19. jim_thompson5910
    • one year ago
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    I'm just saying that not all inverses are parallel

  20. anonymous
    • one year ago
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    No i know that, but are they in this scenario?

  21. anonymous
    • one year ago
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    Are the two equations inverses? I wouldn't think so because they aren't equal to x... Or am I wrong

  22. jim_thompson5910
    • one year ago
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    oh you mean y=2x+2 and y=2x-2?

  23. anonymous
    • one year ago
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    Yeah

  24. jim_thompson5910
    • one year ago
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    well you just found the inverse of y = 2x+2 was y = (1/2)x-1 so it is NOT y=2x-2

  25. jim_thompson5910
    • one year ago
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    y=2x+2 and y=2x-2 aren't inverses of each other

  26. anonymous
    • one year ago
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    Oh ok. Yeah, that's what I thought, but I just wanted to make sure. Do you think you could help me with another problem?

  27. anonymous
    • one year ago
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    Another problem that also has to do with inverse functions...?

  28. jim_thompson5910
    • one year ago
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    go ahead

  29. anonymous
    • one year ago
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    Find the inverse of each function. Then use the definition of inverse functions to verify that the two functions are inverses. 1. f(x) = -3x+3

  30. anonymous
    • one year ago
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    I know that the inverse for this one is f -1(x)=3-x/3

  31. anonymous
    • one year ago
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    The other function is g(x)=0.25x+.6

  32. jim_thompson5910
    • one year ago
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    use parenthesis and say (3-x)/3

  33. jim_thompson5910
    • one year ago
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    keep in mind that 3-x/3 without parenthesis means \(\LARGE 3 - \frac{x}{3}\)

  34. anonymous
    • one year ago
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    Ok. And the inverse for the second one is f-1(x)=-4(.6-x) right?

  35. anonymous
    • one year ago
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    Would I have to plug them into each other to see if they are inverses following the definition of inverse functions?

  36. jim_thompson5910
    • one year ago
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    y=0.25x+0.6 has the inverse y = 4(x-0.6) or y = 4x-2.4

  37. jim_thompson5910
    • one year ago
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    yeah you need to confirm that f(g(x)) = x and g(f(x)) = x

  38. anonymous
    • one year ago
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    ok, so what would I do next?

  39. anonymous
    • one year ago
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    Ok. and they are not inverses right?

  40. jim_thompson5910
    • one year ago
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    which 2?

  41. anonymous
    • one year ago
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    there's more than two?

  42. jim_thompson5910
    • one year ago
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    I'm lost about what you're asking

  43. anonymous
    • one year ago
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    You asked me which two

  44. anonymous
    • one year ago
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    What does that mean?

  45. anonymous
    • one year ago
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    I apologize. I just don't understand this

  46. jim_thompson5910
    • one year ago
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    so you're given 2 functions, right? which 2 functions are you given again?

  47. anonymous
    • one year ago
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    I don't know

  48. anonymous
    • one year ago
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    Would it be the two inverses of the functions?

  49. jim_thompson5910
    • one year ago
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    f(x) = -3x+3 and g(x)=0.25x+.6 right?

  50. anonymous
    • one year ago
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    Yes

  51. jim_thompson5910
    • one year ago
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    so if you can show that f(g(x)) = x and g(f(x)) = x are both true, then you have proven they are inverses of each other

  52. anonymous
    • one year ago
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    ok. Thank you for your help.. I'll post another question if I need help.

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