Composition and Identity of functions

[sfeld]

f(x) = 3x + 2 and g(x) = x + 5

f[g(x)] but some how this equals 3x + 17? please show me.
g[f(x)] I know this would equal 3x + 7


Thanks <3

 

[matt grime]

a function takes the input, performs some operation and gives an output.

f takes the input, multiplies by 3 and adds 2, now what's the input?

 

[HallsofIvy]

f(x)= 3x+ 2 MEANS "what ever is inside the parentheses, multiply it by 3 and then add 2. So f(g(x))= f(x+5) means- multiply x+5 by 3 and then add 2: f(g(x))= 3(x+5)+ 2= what?

g(x)= x+ 5 MEANS "whatever is inside the parentheses, add 5 to it". g(f(x))= g(3x+2) MEANS "add 5 to 3x+ 2". What is that?

 

[Alkatran]

f(x) = 3x + 2
g(x) = x + 5
f(g(x)) = ?

First off, let's make things easier for you and say that:
y = g(x)
which means:
f(g(x)) = f(y)

Now what is y?
y = g(x) = x + 5
And what is f(y)?
f(y) = 3y + 2
since y = g(x) = x + 5 we can replace y with x + 5
3y + 2 = 3(x + 5) + 2
Then take x + 5 out of paratheses:
3(x + 5) + 2 = 3x + 15 + 2 = 3x + 17