anonymous
  • anonymous
Find f(x) and g(x) so that the function can be described as y = f(g(x)). y =(4/x^2) + 9
Mathematics
jamiebookeater
  • jamiebookeater
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Michele_Laino
  • Michele_Laino
I think that a possible choice, can be this: \[\begin{gathered} g\left( x \right) = {x^2} \hfill \\ f\left( x \right) = \frac{4}{x} + 9 \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
we have: \[\Large f\left( {g\left( x \right)} \right) = \frac{4}{{g\left( x \right)}} + 9 = ...?\]
anonymous
  • anonymous
my choices are A.f(x)= x+9 g(x)= 4/x^2 B.f(x)= x g(x)= (4/x)+9 C.f(x)= 1/x g(x)= 4/x)+9 D.f(x)= 4/x^2 g(x)= 9

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Michele_Laino
  • Michele_Laino
I consider case A: \[\Large f\left( {g\left( x \right)} \right) = g\left( x \right) + 9 = ...\] please substitute g(x9= 4/x^2, what do you get?
Michele_Laino
  • Michele_Laino
oops..g(x)=4/x^2, what do you get?
anonymous
  • anonymous
would it be f(x)= x+9
Michele_Laino
  • Michele_Laino
yes! it is, so we can write: \[\Large f\left( {g\left( x \right)} \right) = g\left( x \right) + 9\]
anonymous
  • anonymous
ohh okay!
anonymous
  • anonymous
and how would i get a y value?
Michele_Laino
  • Michele_Laino
you have to replace g(x) with its definition 4/x^2
anonymous
  • anonymous
f(g(x))=g(x)+9 = f(g(x))=(4/x^2)+9
Michele_Laino
  • Michele_Laino
that's right!
anonymous
  • anonymous
thank you so much!
Michele_Laino
  • Michele_Laino
:)

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