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anonymous

  • one year ago

Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u). y=e^7 rootx would it be (g(x),f(u))= (e^x, 7rootx)?

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  1. freckles
    • one year ago
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    \[y=e^{\sqrt[7]{x}}\]?

  2. anonymous
    • one year ago
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    yes

  3. anonymous
    • one year ago
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    wait n, ill draw it

  4. freckles
    • one year ago
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    it looks like you have identified things a bit backwards

  5. anonymous
    • one year ago
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    |dw:1433723874162:dw|

  6. anonymous
    • one year ago
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    the 7 and the square root are being multiplied

  7. freckles
    • one year ago
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    \[y=e^{7 \sqrt{x}}\] you mean this?

  8. anonymous
    • one year ago
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    yes

  9. freckles
    • one year ago
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    say we have \[f(x)=e^x\] what would you get if I asked you to find \[f(7 \sqrt{x})=?\]

  10. freckles
    • one year ago
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    \[f( \text{ twinkie }-\text{ star})=e^{\text{ twinkie}-\text{ star}}\]

  11. freckles
    • one year ago
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    just giving you example of how to do what I asked if you were having trouble

  12. anonymous
    • one year ago
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    would it be (7-e^x)=e^(7-e^x)?

  13. freckles
    • one year ago
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    |dw:1433713458136:dw|

  14. freckles
    • one year ago
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    |dw:1433713475816:dw|

  15. freckles
    • one year ago
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    |dw:1433713493869:dw|

  16. freckles
    • one year ago
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    you replace old input with new input

  17. freckles
    • one year ago
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    so wherever there is the input value x you replace it with what you are trying to input currently

  18. freckles
    • one year ago
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    I hope this makes it more clear what the inside and outside function are

  19. freckles
    • one year ago
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    Here is an example: \[y=2^{5x-7x^2} \\ \text{ outside function }=2^x \\ \text{ inside function }=5x-7x^2 \\ y=f(g(x)) \\ \text{ so } \\ f(x)=2^x \\ g(x)=5x-7x^2 \\ \text{ so we have }f(g(x))=f(5x-7x^2)=2^{5x-7x^2}\]

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