Given f(x) and g(x), please find (fog)(X) and (gof)(x) f(x) = 2x g(x) = x+3
(fog)(x) = 2x + 6
(gof)(x) = 2x + 3
- print Print
- list Cite
Expert Answers
calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
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
Related Questions
- If f(x) = 2x-3 and g(x) = x+1 find fog(3) and gof(-2)?
- 1 Educator Answer
- given that f(x)=√x and g(x)=x+1 find fog find gof
- 1 Educator Answer
- If f(x) = 2x-3 and g(x) = x^2 -2 find fog(x) and gof(x).
- 2 Educator Answers
- if f(x)=2x-3 and fg(x)=2x+1,find g(x)
- 1 Educator Answer
- Find the derivative of fog(x) is f(x)= 2x-3 and g(x) = x^2-2
- 2 Educator Answers
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
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
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
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`
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
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.
Student Answers