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Fudgin [204]
3 years ago
14

Find f(x) and g(x) so that the function can be described as y = f(g(x)). y = Four divided by x squared. + 9

Mathematics
1 answer:
Igoryamba3 years ago
5 0

•   Interpretation I:

Find f and g, so that

                           4
(f o g)(x)  =  —————
                       x² + 9


Well, there is more than one possibility.

                                                     4
For instance, It can be:  f(x)  =  ——  and  g(x) = x² + 9,
                                                     x


and then you have

                          
(f o g)(x)  =  f[ g(x) ]

                         4
(f o g)(x)  =  ————
                       g(x)


                         4
(f o g)(x)  =  —————        ✔
                      x² + 9

                                                                                    4
Another possibility for that composition:   f(x)  =  —————  and  g(x) = x²,
                                                                                 x + 9

and for those, you get

(f o g)(x)  =  f[ g(x) ]

                             4
(f o g)(x)  =  ———————
                     [ g(x) ]² + 9

                           4
(f o g)(x)  =  —————          ✔
                       x² + 9


As you can see above, there are many ways to find f and g, so the composition of those is  (f o g)(x) = 4/(x² + 9).

—————

•  Interpretation II:

Find f and g, so that

                      4
(f o g)(x)  =  ——  +  9
                      x²

                                                            4
It can be:   f(x) = x + 9  and  g(x)  =  ——
                                                            x²

and then you have

(f o g)(x) = f[ g(x) ]

(f o g)(x) = g(x) + 9

                     4
(f o g)(x)  =  ——  +  9
                     x²

                                                                             2
or it could be also:   f(x) = x² + 9  and  g(x)  =  ——
                                                                             x


and you have again

(f o g)(x) = f[ g(x) ]

(f o g)(x) = [ g(x) ]² + 9

(f o g)(x) = [ 2/x ]² + 9

(f o g)(x) = (2²/x²) + 9

                      4
(f o g)(x)  =  ——  +  9          ✔
                     x²


As you can see above, there are many ways to find f and g, so the composition of those is  (f o g)(x) = (4/x²) + 9.


I hope this helps. =)


Tags:  <em>composite functions rational quadratic linear function algebra</em>

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