## 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)?

1. freckles

$y=e^{\sqrt[7]{x}}$?

2. anonymous

yes

3. anonymous

wait n, ill draw it

4. freckles

it looks like you have identified things a bit backwards

5. anonymous

|dw:1433723874162:dw|

6. anonymous

the 7 and the square root are being multiplied

7. freckles

$y=e^{7 \sqrt{x}}$ you mean this?

8. anonymous

yes

9. freckles

say we have $f(x)=e^x$ what would you get if I asked you to find $f(7 \sqrt{x})=?$

10. freckles

$f( \text{ twinkie }-\text{ star})=e^{\text{ twinkie}-\text{ star}}$

11. freckles

just giving you example of how to do what I asked if you were having trouble

12. anonymous

would it be (7-e^x)=e^(7-e^x)?

13. freckles

|dw:1433713458136:dw|

14. freckles

|dw:1433713475816:dw|

15. freckles

|dw:1433713493869:dw|

16. freckles

you replace old input with new input

17. freckles

so wherever there is the input value x you replace it with what you are trying to input currently

18. freckles

I hope this makes it more clear what the inside and outside function are

19. freckles

Here is an example: $y=2^{5x-7x^2} \\ \text{ outside function }=2^x \\ \text{ inside function }=5x-7x^2 \\ y=f(g(x)) \\ \text{ so } \\ f(x)=2^x \\ g(x)=5x-7x^2 \\ \text{ so we have }f(g(x))=f(5x-7x^2)=2^{5x-7x^2}$