SOLUTION: Hi there My question is: For each pair of functions, obtain a formula for f(g(x)) and also for g(f(x)) f(x)=2x+3 g(x)=3x+2 Can you show ALL your working to perhaps help m

Algebra ->  Rational-functions -> SOLUTION: Hi there My question is: For each pair of functions, obtain a formula for f(g(x)) and also for g(f(x)) f(x)=2x+3 g(x)=3x+2 Can you show ALL your working to perhaps help m      Log On


   

Question 1020946: Hi there
My question is: For each pair of functions, obtain a formula for f(g(x)) and also for g(f(x))
f(x)=2x+3
g(x)=3x+2
Can you show ALL your working to perhaps help me to understand better - would be very much appreciated
Thanks so much
Found 2 solutions by FrankM, rothauserc:
Answer by FrankM(1040) About Me  (Show Source):
You can put this solution on YOUR website!
I am going to borrow a strategy from the Calculus for dummies author -
For f(g(x)) think of
f(x)=2x+3 as f(stuff)=2(stuff)+3 in other words, the f(stuff ) function says to take that stuff, double it and add 3.
but here, stuff=g(x)=3x+2
so f(stuff)=2(stuff)+3 just needs the substitution, stuff=3x+2 and
f(g(x))=2(3x+2)+3 = 6x+7
Now, let's check real quick with one substitution X=1.
f(x)=2x+3
g(x)=3x+2
g(1)=3(1)+2=5
f(5)=2(5)+3=13
f(g(1))=6x+7= 13 (check)
Now the next one needs less explaining.
g(f(x))
g(f(x))=3(2x+3)+2= 6x+11 << don't forget to check.

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
f(g(x) means apply g(x) first then apply f(x)
:
: we are given f(x)=2x+3 and g(x)=3x+2
:
f(3x+2) = 2(3x+2)+3
: we substitute g(x) for x in f(x)
f(g(x) = 6x+4+3 = 6x+7
:
g(2x+3) = 3(2x+3)+2
g(f(x)) = 6x+9+2 = 6x+11
: