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Let f(x) = 2x - 3 and g(f(x)) = 5-4x. Find g(4).

coolcoolcool

 Jul 22, 2017
edited by Guest  Jul 22, 2017
edited by Guest  Jul 22, 2017
 #1
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g( f(x) )  =  5 - 4x

 

We want to find  g(4)  , that is, we want to find  g  when...

 

f(x)  =  4

                             Since  f(x)  =  2x - 3  , we can replace  f(x)  with  2x - 3  .

2x - 3  =  4

                             Add  3  to both sides.

2x  =  7

                             Divide both sides by  2  .

x  =  7/2

 

Now we know that when  x = 7/2  , f(x)  =  4 .

 

g( f(x) )  =  5 - 4x

                                              Replace every instance of  x  with  7/2  .

g( (f(7/2) )  =  5 - 4(7/2)

                                              Since  f(7/2)  =  4 , we can say...

g(4)  =  5 - 4(7/2)

 

g(4)  =  -9

 Jul 22, 2017

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