Question

Given f(x) and g(x), please find (fog)(X) and (gof)(x)
f(x) = 2x   g(x) = x+3

Accepted Answer

(fog)(x) = 2x + 6
(gof)(x) = 2x + 3

Answer

We have given f(x) = 2x and g(x) = x+3
We have to find, (fog)(x) = f(g(x)) and (gof)(x) = g(f(x))
1. For finding (fog)(x) = f(g(x)), we have to replace x by g(x) in f(x)
    So, (fog)(x) = f(g(x)) = 2*g(x) = 2*(x+3) = 2x+6
2. For finding (gof)(x) = g(f(x)), we have to replace x by f(x) in g(x) 
    So, (gof)(x) = g(f(x)) = f(x)+3 = 2x+3
So, finally (fog)(x) = 2x+6
               (gof)(x) = 2x+3

Answer

Here f(x) and g(x)  is defined .We are asked to compute the composition functions (fog)(x) and (gof)(x).
Now (fog)(x)
=f(g(x))
=f(x+3)
=2(x+3)
=2x+6
Also (gof)(x)
=g(f(x))
=g(2x)
=2x+3

Answer

I like to write composition problems such as this one as g(f(x)) and f(g(x)) rather than the (fog)(x) and (gof)(x).  I do this because it reminds me the order in which to solve the problem.  When we are finding g(f(x)), I want to work inside out.  This means since f(x) is the inner most part of the equation, I want to take f(x) and plug it into g(x), as shown below:
 
g(f(x)) = g(2x)  <----  I replaced the f(x) with 2x because they are equal
In the g(x) equation, we need to replace the x with 2x, so:
g(2x) = 2x + 3
There is nothing to simplify in the above equation, so we now know that g(f(x)) = 2x + 3
 
The process is similar for f(g(x)).
f(g(x)) = f(x+3) <------ Again, working inside out.....g(x) is replaced with x + 3 because they are equal.
f(x +3) = 2(x + 3) <------x in the f(x) equation is replaced with x + 3
           = 2x + 6 < ----- distributing the 2 to the x and the 3 gets the final answer
so f(g(x)) = 2x + 6

Answer

So remember that (f@g)(x)=f(g(x))
so subbing in g(x), we get
 f(x+3)
Replacing each x in f with x+3, we get
2(x+3)
(f@g)(x)=2x+6

For (g@f)(x)=g(f(x))
We have that (g@f)(x)=g(f(x))
=g(2x)
(g@f)(x)=2x+3

Answer

To calculate the compositions of the functions, we'll apply the rule:
(fog)(x) = f(g(x)) (f of g of x)
It is obvious that we'll substitute x by the expression of g(x) and we'll get:
f(g(x)) = f(x+3) = 2*(x+3)
We'll remove the brackets and we'll have:
(fog)(x) = 2x + 6
Now, we'll calculate  (gof)(x).
 (gof)(x) = g(f(x)) (g of f of x)
It is obvious that we'll substitute x by the expression of f(x) and we'll get:
g(f(x)) = g(2x) = 2x + 3
(gof)(x) = 2x + 3

Answer

f(x) = 2x. g(x) = x+3.
To find (fog)(x) and (gof)(x).
Solution:
f(x) = 2x. g(x) = x+3.
Substitute g(x) for x in f(x) to get (fOg)(x): 
f((g(x)) = 2 (g(x) = 2(x+3) = 2x+6.
To get (gof)(x), substitute  f(x) for x in g(x):
(gof)(x) =  (2x) + 3 = 2x+3.

Answer

f(x) = 2x
g(x) = x + 3
First let us find (fog)(x)
(fog)(x) = f(g(x)
             = f(x+3)
               = 2(x+3)
               = 2x + 6
==> (fog)(x) = 2x + 6
Now let us find (gof)(x):
(gof)(x) = g(f(x)
            = g(2x)
           = 2x + 3
==> (gof)(x) = 2x + 3

Math

Given f(x) and g(x), please find (fog)(X) and (gof)(x) f(x) = 2x g(x) = x+3

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