If f(x)=2x+6 and g(x)= -8x what is g(f(4))

Question

Composition of polynomial functions

Answer 1

The problem asks you to find g(f(4)).  First, you must find f(4)  [note: work from the inside outward).

 

  f(4) = 2(4) + 6             [find f(x) when x=4]

   f(4) = 8 + 6

   f(4) = 14

 

Now, you may find g(14).         [replace f(4) with 14 to find g(x) when x=14]

  g(14) = -8(14)

  g(14) = -112

 

So, g(f(4)) = -112

 

PLZ realize that f(x) and g(x) are functions of two different values for x.  Of course, with any function, the independent variable x may have any legal value (in the domain of the function).

Answer 2

f(g(x)) = 2(g(x)) + 6

           = 2(-8x) +6

 

f(g(4)) = 2(-8•4) +6

           =2(-32) +6

           =-64 +6

           = -58.