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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

tutor4u's profile pic

tutor4u | College Teacher | (Level 1) eNoter

Posted on

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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