anonymous
  • anonymous
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)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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zzr0ck3r
  • zzr0ck3r
ok do you know what composition is?
anonymous
  • anonymous
yep! but i'm a little confused especially on verification
zzr0ck3r
  • 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 \(f(2x)=\sqrt{2x}\)

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zzr0ck3r
  • zzr0ck3r
what do we need \(g(x) \) to be so that we have \(f(g(x)) = \sqrt{3x-4}\)?
anonymous
  • anonymous
sqrtx?
zzr0ck3r
  • zzr0ck3r
we are letting \(f(x) = \sqrt{x}\).
zzr0ck3r
  • zzr0ck3r
hint: \(f(\color{blue}{g(x)})= \sqrt{\color{blue}{3x-4}}\)
zzr0ck3r
  • zzr0ck3r
what is \(g(x) = \)?
anonymous
  • anonymous
oh! √x ?
zzr0ck3r
  • zzr0ck3r
no
zzr0ck3r
  • zzr0ck3r
you are just saying the same thing over and over...
anonymous
  • anonymous
wait sorry
anonymous
  • anonymous
i wasn't paying attention
zzr0ck3r
  • zzr0ck3r
right
anonymous
  • anonymous
3x-4
zzr0ck3r
  • zzr0ck3r
correct
zzr0ck3r
  • zzr0ck3r
ok, so do you see why we choose \(f(x) = \sqrt{x}\)?
anonymous
  • anonymous
yeah i get that now haha
zzr0ck3r
  • zzr0ck3r
the last part makes no sense. It is not true that \(f(g(x))= f(x)\)
anonymous
  • anonymous
it then says f(gx)) = (sqrt3x-4) though so is it still totally wrong

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