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anonymous

  • one year ago

Given the parent functions f(x) = log10 x and g(x) = 5x − 2, what is f(x) • g(x)?

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  1. anonymous
    • one year ago
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    @Astrophysics

  2. Astrophysics
    • one year ago
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    \[f(x)g(x) = \log_{10}x (5x-2)\]

  3. Astrophysics
    • one year ago
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    You're just multiplying the functions

  4. anonymous
    • one year ago
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    Thanks! Can I ask one more?

  5. anonymous
    • one year ago
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    If f(x) = log2 (x + 4), what is f−1(3)?

  6. Astrophysics
    • one year ago
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    The \[f^{-1}\] represents inverse

  7. anonymous
    • one year ago
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    yes:)

  8. Astrophysics
    • one year ago
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    To find the inverse: Replace f(x) with y Switch x's and y's, so put x where y is and x where y is. Solve for y Replace y with f^-1(x)

  9. Astrophysics
    • one year ago
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    Once you find the inverse just plug in 3 into the function and evaluate :-)

  10. anonymous
    • one year ago
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    y=log2(x+4)

  11. Astrophysics
    • one year ago
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    good keep going

  12. anonymous
    • one year ago
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    x=log2(y+4)

  13. Astrophysics
    • one year ago
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    right

  14. anonymous
    • one year ago
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    im confused on how to solve for "Y"

  15. Astrophysics
    • one year ago
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    Since it's \[\log_2\] as the base we will have to take the power of 2 to on both sides so the following \[\huge 2^x = 2^{\log_2(y+4)} \implies 2^x = y+4\]

  16. anonymous
    • one year ago
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    hmm then wouldnt we have to get y alone?

  17. anonymous
    • one year ago
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    Would the answer be 8?

  18. Loser66
    • one year ago
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    f(a) =b , hence \(f^{-1} (b) =a\) ok?

  19. Loser66
    • one year ago
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    we need find \(f^{-1} (3) \) of \(f(x) = log 2(x+4)\), right? That is just let log 2(x+4) =3, and solve for x.

  20. Astrophysics
    • one year ago
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    You can do either way you should get same result

  21. anonymous
    • one year ago
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    2?

  22. Astrophysics
    • one year ago
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    No, \[y=2^x-4 \implies f^{-1}(x) = 2^x-4 \implies f^{-1}(3) = 2^3-4\]

  23. anonymous
    • one year ago
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    oh! okay so then I got, 4

  24. Loser66
    • one year ago
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    confirm: \(log (2(x+4))\) or (x+4)*log 2??

  25. Astrophysics
    • one year ago
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    Yes, 4 sounds betters :)

  26. anonymous
    • one year ago
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    2x2x2=4x2=8 8-4=4 :)

  27. Astrophysics
    • one year ago
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    I think the original question was \[\log_2(x+4)\] right?

  28. anonymous
    • one year ago
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    yes

  29. Astrophysics
    • one year ago
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    Ok we're good then

  30. Astrophysics
    • one year ago
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    Thanks @Loser66

  31. anonymous
    • one year ago
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    yay! Thanks guysss:)

  32. Loser66
    • one year ago
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    ok, clear.

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