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anonymous

  • one year ago

F(x)=ln(x) g(x)=e^x+1. F(g(x)) must then be ln(e^x+1) right? Can you simplify this?

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  1. dumbcow
    • one year ago
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    is that e^(x+1) ?

  2. dumbcow
    • one year ago
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    e^x and ln(x) are inverse functions so: \[\ln(e^x) = x\]

  3. anonymous
    • one year ago
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    yes you are right

  4. anonymous
    • one year ago
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    No, g(x) is just e^x+1, as if it was 1+e^x without any parenthesis

  5. anonymous
    • one year ago
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    \[f(g(x))= \ln(e ^{x}+1)\]

  6. anonymous
    • one year ago
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    let me know if u need furthur help :)

  7. anonymous
    • one year ago
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    oh btw you cant simplify further

  8. anonymous
    • one year ago
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    or maybe write Near x=0, I suppose you could expand e^x,

  9. anonymous
    • one year ago
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    because ln(1) = 0 and also ln(e^x) is also 0 because they are inverse pairs

  10. anonymous
    • one year ago
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    So that makes it x+1 in the end. But the reverse, g(f(x)) = e^ln(x)+1 will also become x+1? Right?

  11. anonymous
    • one year ago
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    Ah, ok :)

  12. anonymous
    • one year ago
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    |dw:1442478053901:dw|

  13. anonymous
    • one year ago
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    yes

  14. anonymous
    • one year ago
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    Thanks!

  15. anonymous
    • one year ago
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    no problem just tag if you need any further help :)

  16. anonymous
    • one year ago
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    srry ln(e^x)= x not zero

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