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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)

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  1. zzr0ck3r
    • one year ago
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    ok do you know what composition is?

  2. anonymous
    • one year ago
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    yep! but i'm a little confused especially on verification

  3. zzr0ck3r
    • one year ago
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    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
    • one year ago
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    what do we need \(g(x) \) to be so that we have \(f(g(x)) = \sqrt{3x-4}\)?

  5. anonymous
    • one year ago
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    sqrtx?

  6. zzr0ck3r
    • one year ago
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    we are letting \(f(x) = \sqrt{x}\).

  7. zzr0ck3r
    • one year ago
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    hint: \(f(\color{blue}{g(x)})= \sqrt{\color{blue}{3x-4}}\)

  8. zzr0ck3r
    • one year ago
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    what is \(g(x) = \)?

  9. anonymous
    • one year ago
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    oh! √x ?

  10. zzr0ck3r
    • one year ago
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    no

  11. zzr0ck3r
    • one year ago
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    you are just saying the same thing over and over...

  12. anonymous
    • one year ago
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    wait sorry

  13. anonymous
    • one year ago
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    i wasn't paying attention

  14. zzr0ck3r
    • one year ago
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    right

  15. anonymous
    • one year ago
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    3x-4

  16. zzr0ck3r
    • one year ago
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    correct

  17. zzr0ck3r
    • one year ago
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    ok, so do you see why we choose \(f(x) = \sqrt{x}\)?

  18. anonymous
    • one year ago
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    yeah i get that now haha

  19. zzr0ck3r
    • one year ago
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    the last part makes no sense. It is not true that \(f(g(x))= f(x)\)

  20. anonymous
    • one year ago
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    it then says f(gx)) = (sqrt3x-4) though so is it still totally wrong

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