Find the domain of the composite function fog (x) if f(x)= 2x+1; g(x)= x +4
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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
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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!!
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