anonymous
  • anonymous
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)?
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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freckles
  • freckles
\[y=e^{\sqrt[7]{x}}\]?
anonymous
  • anonymous
yes
anonymous
  • anonymous
wait n, ill draw it

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freckles
  • freckles
it looks like you have identified things a bit backwards
anonymous
  • anonymous
|dw:1433723874162:dw|
anonymous
  • anonymous
the 7 and the square root are being multiplied
freckles
  • freckles
\[y=e^{7 \sqrt{x}}\] you mean this?
anonymous
  • anonymous
yes
freckles
  • freckles
say we have \[f(x)=e^x\] what would you get if I asked you to find \[f(7 \sqrt{x})=?\]
freckles
  • freckles
\[f( \text{ twinkie }-\text{ star})=e^{\text{ twinkie}-\text{ star}}\]
freckles
  • freckles
just giving you example of how to do what I asked if you were having trouble
anonymous
  • anonymous
would it be (7-e^x)=e^(7-e^x)?
freckles
  • freckles
|dw:1433713458136:dw|
freckles
  • freckles
|dw:1433713475816:dw|
freckles
  • freckles
|dw:1433713493869:dw|
freckles
  • freckles
you replace old input with new input
freckles
  • freckles
so wherever there is the input value x you replace it with what you are trying to input currently
freckles
  • freckles
I hope this makes it more clear what the inside and outside function are
freckles
  • freckles
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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