Find the domain of the composite function fog (x) if f(x)= 2x+1; g(x)= x +4
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,554 answers
starTop subjects are Math, Science, and Business
The function f(x)= 2x+1 and g(x)= x +4
fog(x) = f(g(x)) = f(x + 4)
=> 2(x + 4) + 1
=> 2x + 8 + 1
=> 2x + 9
The domain of fog(x) is the set of all real numbers R
Related Questions
- Given f(x) and g(x), please find (fog)(X) and (gof)(x) f(x) = 2x g(x) = x+3
- 1 Educator Answer
- if f(x)=2x-3 and fg(x)=2x+1,find g(x)
- 1 Educator Answer
- If f(x)=x+4 and h(x)=4x-1, find a function g such that g(f(x)) = h(x).
- 2 Educator Answers
- If f(x) = 2x-3 and g(x) = x+1 find fog(3) and gof(-2)?
- 1 Educator Answer
- Given the function f(x)=2x-3, find the function g(x)=f(x+1)+f(x-1)?
- 1 Educator Answer
We have given the functions as f(x) = 2x + 1 and g(x) = x + 4
For finding (fog)(x), we need to understand what exactly we need to do here.
Let me write some equivalent function of the given function first.
(fog)(x) = f( g(x) )
That means in place of x, we have given the function as g(x).
So, we need to first replace the function g(x) by its given value. i.e. g(x) = x + 4
by replacing, we will get
(fog)(x) = f( g(x) ) = f( (x + 4) ).
Now, we can see that in place of x, we have given x + 4. so, replace the value of x by x + 4 in the given original function f(x) = 2x + 1
We will get
(fog)(x) = f( g(x) ) = f( (x + 4) )
f(x) = 2x + 1
f( (x + 4) ) = 2*( (x + 4) ) + 1
using foil = 2x + 8 + 1
= 2x + 9
(fog)(x) = 2x + 9
As it is simple a linear equation. so, domain will be defibned for all real values R.
Hope this will help you!!
Student Answers