anonymous
  • anonymous
find the {g(f(x))}and {f(g(x))}. are they equal? g(x)=x-2 f(x)=x^2+x-12
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Hello, you just have to compose the functions. For the first one:\[g(f(x))=[f(x)]-2=[x^2+x-12]-2\]Do you see how f(x) took the place of x in g(x)=x-2?
anonymous
  • anonymous
So you'd keep going to simplify:\[g(f(x))=x^2+x-14\]
anonymous
  • anonymous
For the other one,\[f(g(x))=[g(x)]^2+[g(x)]-12=[x-2]^2+[x-2]-12\]

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anonymous
  • anonymous
So\[f(g(x))=x^2-4x+4+x-2-12= x^2+3x-10\]
anonymous
  • anonymous
When you compare the results, they're not the same function.
anonymous
  • anonymous
They're trying to show you that in general,\[f(g(x)) \ne g(f(x))\]
anonymous
  • anonymous
yeah, you're welcome.

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