anonymous
  • anonymous
Need help with a discrete math problem.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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dape
  • dape
Have you solved any of them? Do you know how to take the composite of two functions?
anonymous
  • anonymous
I am thinking f of g would be would be like f(g(x))

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anonymous
  • anonymous
so for (a) we must be looking at f(f(x)) if that is right
anonymous
  • anonymous
But I don't understand the mapping R into R part
anonymous
  • anonymous
Mapping from R to R just means that its domain is a subset of the real numbers and its range is a subset of the real numbers
anonymous
  • anonymous
ah, that makes sense.
anonymous
  • anonymous
What about writing k(x) in terms of x
anonymous
  • anonymous
Would that just be for (a) k(x) = (x^2)^2
dape
  • dape
It just means that you should have k equal something involving only x's. Yeah, that's right.
anonymous
  • anonymous
ok cool I'm sure I can figure out the rest then. Thanks for the help! :)
anonymous
  • anonymous
b. k(x) = g(g(x)) = root((root(x^2)+1)^2 + 1)
dape
  • dape
Yup, and that simplifies to \(\sqrt{x^2+2}\).
anonymous
  • anonymous
ah ok, awesome
anonymous
  • anonymous
c. k(x) = h(g(x)) = 3(root(x^2+1))
anonymous
  • anonymous
d. k(x) = g(h(x) = root((3x - 1)^2 + 1)
anonymous
  • anonymous
e. k(x) = f(g(h(x))) = (root((3x - 1)^2 + 1))^2
dape
  • dape
They are all correct except c. And e can be simplified.
anonymous
  • anonymous
c. 3root(x^2+1)
dape
  • dape
You are still missing the -1 at the end ;)
dape
  • dape
\(h(x)=3x-1\)
anonymous
  • anonymous
3(root(x^2+1) - 1)
anonymous
  • anonymous
ah I see
anonymous
  • anonymous
so 3root(x^2)
dape
  • dape
Nope, the 1's doesn't cancel, \(3\sqrt{x^2-1}-1\neq3\sqrt{x^2}\).
anonymous
  • anonymous
oh woops
anonymous
  • anonymous
can it be simplified then?
dape
  • dape
Nope
anonymous
  • anonymous
ah ok then e can be simplified?
dape
  • dape
Yeah, since the f(x) takes away the square-root sign of g(x).
dape
  • dape
\(f(g(x))=f(\sqrt{x^2+1})=(\sqrt{x^2+1})^2=x^2+1\)
dape
  • dape
Then you can put \(h(x)\) into that.
anonymous
  • anonymous
should I multiply out the squared part or just leave it?
anonymous
  • anonymous
looks simpler to just leave it so (3x - 1)^2 + 1
dape
  • dape
Yeah, it's a matter of taste, I would probably multiply it out to get the pure polynomial form of it.
anonymous
  • anonymous
ah ok, makes sense.
anonymous
  • anonymous
9x^2 - 6x + 2
anonymous
  • anonymous
Alrighty thanks so much for the help :D
dape
  • dape
No problem =)

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