If f(x)=2x and g(x)=x+5, find (fog)(x)

Question

I need to find fog and x in this equation if x equals 2 and g equals x+5 then I need to find fog x

Answer 1

Iqra, I think you are getting some things confused, which is OK. Let's see if I can help.

 

Let's say that f(x)= 2x + 5. We cannot find a value for x with just this. Instead, we would say what is the value of 2x + 5 if x = 4 (or some other number). The short way to write that is f(4). 

 

So, if f(x) = 2x + 5, and we want to know f(4), we put 4 in for x.

 

f(4) = 2(4) + 5 = 13.

 

f(6) = 2(6) + 5 = 17.

 

Instead, we have f(x) = 2x and g(x) = x + 5. Another way to write fog(x) is f(g(x)).

 

This means that for each x in f(x), we are going to plug in g(x).

 

f(g(x)) = 2(x + 5) = 2x + 10.

 

That's it! 

Answer 2

f(x) = 2x

g(x) = x+5

 

The composite function, (fog)(x), is sometimes written as f(g(x)).  To determine the composite, simply replace the x in f(x) with g(x):

 

f(x) = 2x

 

(fog)(x) = 2g(x)

 

   = 2(x+5)

 

   = 2x +10