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anonymous

  • one year ago

Use the functions f(x) = 5x − 12 and g(x) = 11x + 2 to complete the function operations listed below. Part A: Find (f + g)(x). Show your work. (3 points) Part B: Find (f ⋅ g)(x). Show your work. (3 points) Part C: Find f[g(x)]. Show your work. (4 points)

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  1. anonymous
    • one year ago
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    @Keigh2015

  2. anonymous
    • one year ago
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    @phi

  3. anonymous
    • one year ago
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    Hey

  4. Keigh2015
    • one year ago
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    do you have an idea for it yet?

  5. phi
    • one year ago
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    (f + g)(x) that is short of adding f(x) + g(x)

  6. anonymous
    • one year ago
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    so add 5x − 12 And 11x + 2

  7. phi
    • one year ago
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    and f(x)+g(x) is short for: write down the "formula" for f(x) and add it to the "formula" for g(x) yes

  8. Keigh2015
    • one year ago
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    yes i believe

  9. phi
    • one year ago
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    B is the same idea except you multiply (use FOIL to multiply it out)

  10. anonymous
    • one year ago
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    let me add the first one real quick hold on

  11. phi
    • one year ago
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    can you do parts A and B?

  12. anonymous
    • one year ago
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    16x−10

  13. phi
    • one year ago
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    yes

  14. anonymous
    • one year ago
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    Yea i think so, ill try could you check my work?

  15. phi
    • one year ago
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    for part C f[g(x)] means "in the formula for f(x), replace "x" with g(x)"

  16. anonymous
    • one year ago
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    for part B i got 55x2−122x−24 i think thats wrong

  17. phi
    • one year ago
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    too bad, I got the same thing.

  18. anonymous
    • one year ago
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    is it?

  19. phi
    • one year ago
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    yes, you did it correctlly

  20. anonymous
    • one year ago
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    ill just put that as the answer, because i honestly have to clue.

  21. anonymous
    • one year ago
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    ooh yay okay

  22. phi
    • one year ago
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    you can check that it is correct. pick a number for x, such as 1 then f(x) = 5x − 12 at x=1 is 5-12= -7 and g(x) = 11x + 2 at x=2 is 11+2 = 13 and -7*13= -91 now use your formula 55x^2−122x−24 at x=1... you get 55 -122 -24 = -91 same number. that does not prove it, but if you did that for a few values, and it always works, it probably is correct.

  23. anonymous
    • one year ago
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    for part c, questions like that confuse me cause i never learned the foil method.

  24. anonymous
    • one year ago
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    @phi

  25. anonymous
    • one year ago
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    @Keigh2015

  26. Keigh2015
    • one year ago
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    that one confuses me too

  27. anonymous
    • one year ago
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    @mathstudent55

  28. phi
    • one year ago
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    but if you FOIL it: ( 5x − 12) (11x+2) F first: 5x*11x = 55x^2 O outer: 5x*2 = 10x I inner: -12*11x = -132x L last: -12*2 = -24 combine the two middle terms 10x-132x = -122 x and the answer is 55x^2 -122x -24

  29. anonymous
    • one year ago
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    @mathstudent55 i need help with part c

  30. phi
    • one year ago
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    part C f[g(x)] first write down f(x)

  31. anonymous
    • one year ago
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    5x − 12

  32. phi
    • one year ago
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    like this f(x)=5x − 12 we want f[g(x)] that means erase the x and replace it with g(x) erase and replace: f( g(x) ) = 5g(x) -12

  33. phi
    • one year ago
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    then replace g(x) with g(x)'s formula (11x + 2) be sure to use the parens

  34. phi
    • one year ago
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    can you replace g(x) in 5g(x) -12 with (11x+2)

  35. anonymous
    • one year ago
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    f( 11x + 2) = 5(11x + 2) -12

  36. anonymous
    • one year ago
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    @phi

  37. phi
    • one year ago
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    yes, but we usually leave the left side in "short form" f(g(x)) and only expand the right side but yes that looks good. you can distribute the 5 (multiply 5 times each thing inside the parens) and simplify the right side a little.

  38. anonymous
    • one year ago
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    x=1\11 ? @phi

  39. phi
    • one year ago
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    the right side is 5(11x + 2) -12 do 5 * 11x + 5*2 to distribute the 5 55x + 10 -12 now simplify 10-12

  40. anonymous
    • one year ago
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    -2?

  41. phi
    • one year ago
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    yes. so part C is f[g(x)]= 55x-2

  42. anonymous
    • one year ago
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    Yay thankyou @phi

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