What is the rule for functions

Question

 If f(x)=4x+7 and g(x)=2x then What is the rule for g(f(x)) and what is the rule for f(g(x))?

Answer 1

ok we're trying to find g(f(x)) it's the composition of two function.. What you need to do is start from the inside out and simplify as you go..

 

g( f(x) ) = g(  4x+7  )   right so all i'm doing is substituting for the variable

             = 2 ( 4x+7 )

             = 8x + 14

 

you can do the same process for f(g(x)).. you get 8x + 7

 

good luck

Answer 2

 

g(f(x)) means to plug f(x) into g(x):

 

g(f(x)) = g(4x+7) = 2(4x+7) = 8x + 14

 

 

f(g(x)) means to plug g(x) into f(x):

 

f(g(x)) = f(2x) = 4(2x) + 7 = 8x + 7