## anonymous one year ago Please help :) Express the following function, F(x), as a composition of two functions, f and g. f(g(x)). F(x)= (sqrt3x-4) Part 1: Find g(x) by identifying the function you are taking the square root of. Part 2: Find f(x) by identifying what you are doing to the function you found in part 1. What function is f(X)? Part 3: Verify that f(g(x))=f(x) f(g(x))=(sqrt3x-4)

1. zzr0ck3r

ok do you know what composition is?

2. anonymous

yep! but i'm a little confused especially on verification

3. zzr0ck3r

suppose we have the function $$f(x) = \sqrt{x}$$ Then $$f(4) = \sqrt{4}=2$$ and $$f(25) = \sqrt{25} = 5$$ and $$f(3) = \sqrt{3}$$ and $$f(2x)=\sqrt{2x}$$

4. zzr0ck3r

what do we need $$g(x)$$ to be so that we have $$f(g(x)) = \sqrt{3x-4}$$?

5. anonymous

sqrtx?

6. zzr0ck3r

we are letting $$f(x) = \sqrt{x}$$.

7. zzr0ck3r

hint: $$f(\color{blue}{g(x)})= \sqrt{\color{blue}{3x-4}}$$

8. zzr0ck3r

what is $$g(x) =$$?

9. anonymous

oh! √x ?

10. zzr0ck3r

no

11. zzr0ck3r

you are just saying the same thing over and over...

12. anonymous

wait sorry

13. anonymous

i wasn't paying attention

14. zzr0ck3r

right

15. anonymous

3x-4

16. zzr0ck3r

correct

17. zzr0ck3r

ok, so do you see why we choose $$f(x) = \sqrt{x}$$?

18. anonymous

yeah i get that now haha

19. zzr0ck3r

the last part makes no sense. It is not true that $$f(g(x))= f(x)$$

20. anonymous

it then says f(gx)) = (sqrt3x-4) though so is it still totally wrong