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If h(x) = f(x)g(x) and f(x) = 2x +5, determine g(x).

 

I'm given h(x) = 6x + 15.

 

I know I can divide h(x) by f(x), but I have no idea on how to continue on from there?

 

Thank you! :)

 Jun 12, 2019
 #1
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\(\ h(x)\ =\ f(x)\cdot g(x)\)

                                          Divide both sides of the equation by  f(x)

\(\dfrac{h(x)}{f(x)}\ =\ g(x)\)

                                          Substitute  6x + 15  in for  h(x)  and substitute  2x + 5  in for  f(x)

\(\frac{6x+15}{2x+5}\ =\ g(x)\)

                                          That is the same as....

\(g(x)\ =\ \frac{6x+15}{2x+5}\)

                                          We can factor  3  out of  6x + 15  because  3(2x + 5)  =  6x + 15

\(g(x)\ =\ \frac{3(2x+5)}{2x+5}\)

                                          Cancel the common factor of  (2x + 5)  in the numerator and denominator.

 

\(g(x)\ =\ 3\)          and note that   2x + 5  ≠  0   so   x  ≠  -5/2

 

So we can say     g(x)  =  3     for all possible values of  x  except  x = -5/2

 Jun 12, 2019

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