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anonymous

  • one year ago

If r(x) = 2 – x2 and w(x) = x – 2, what is the range of (w*r)(x)

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  1. SolomonZelman
    • one year ago
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    is it ` (wº r)(x) `, or is it ` (w • r)(x) ` ?

  2. anonymous
    • one year ago
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    the first one

  3. SolomonZelman
    • one year ago
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    Ok, you know that ` (wº r)(x) ` just means ` w(r(x)) ` in other words, you take the x in the function w(x), and plug in the function r(x) instead of it.

  4. SolomonZelman
    • one year ago
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    w(x)=x-2 r(x)=2-x² ------------- so, you know that: w(\(\small\color{red}{x}\))=\(\small\color{red}{x}\)-2 and therefore: w(\(\small\color{red}{r(x)}\)) =(\(\small\color{red}{2-x^2}\))-2

  5. SolomonZelman
    • one year ago
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    can you simplify the w(r(x)) /

  6. SolomonZelman
    • one year ago
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    ?

  7. anonymous
    • one year ago
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    do you mean solve (w-x^2)-2?

  8. anonymous
    • one year ago
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    2 instead of w

  9. anonymous
    • one year ago
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    my bad

  10. anonymous
    • one year ago
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    if so it would be -x^2

  11. SolomonZelman
    • one year ago
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    yes

  12. SolomonZelman
    • one year ago
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    so (wº r)(x) = -x² and you need to find the range of this

  13. anonymous
    • one year ago
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    ok and how would i do that haha

  14. SolomonZelman
    • one year ago
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    x² \(\small \ge\) 0 (for any real number value of x)

  15. SolomonZelman
    • one year ago
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    so the range of x² is (0,+∞)

  16. SolomonZelman
    • one year ago
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    now, multiply both sides of: x² \(\small \ge\) 0 by -1, and you get

  17. anonymous
    • one year ago
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    -x^2 and 0

  18. SolomonZelman
    • one year ago
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    and what is the sign, \(\small \ge\) or \(\small \le\)

  19. anonymous
    • one year ago
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    <

  20. SolomonZelman
    • one year ago
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    -x² \(\small \le\) 0 like that?

  21. anonymous
    • one year ago
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    yes

  22. SolomonZelman
    • one year ago
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    that is correct

  23. anonymous
    • one year ago
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    yay ty

  24. SolomonZelman
    • one year ago
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    so -x² is at most 0, and can go into any very big negative values

  25. anonymous
    • one year ago
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    mhm

  26. SolomonZelman
    • one year ago
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    so the range of -x² is?

  27. SolomonZelman
    • one year ago
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    well, it is at most 0, so we know that: ,0] and it can go into nagetive infinty so we know that: (-∞, 0]

  28. anonymous
    • one year ago
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    thats it

  29. SolomonZelman
    • one year ago
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    yes

  30. anonymous
    • one year ago
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    i just didnt know how to make a infinity sign haha

  31. SolomonZelman
    • one year ago
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    oh, 1. you click ALT, and hold it 2. click 2 3 6 (respectively) on the number pad on the right side of your keyboard 3. you release the ALT, and get ∞

  32. SolomonZelman
    • one year ago
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    try it yourself

  33. anonymous
    • one year ago
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  34. anonymous
    • one year ago
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    thank you!

  35. SolomonZelman
    • one year ago
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    Yes, and if you use a the code 0 2 1 5 , you get ×

  36. SolomonZelman
    • one year ago
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    and code of 2 4 6 , you get ÷

  37. SolomonZelman
    • one year ago
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    there are many symbols like that. 755 , ≤ 754, ≥ 251, √

  38. SolomonZelman
    • one year ago
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    if you have any questions, I will be happy to answer.

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