Step-by-step explanation:
Step 1: Identify the blanks
[tex]f(x) = \sqrt{x-3}[/tex] and [tex]g(x) = 2x + 4[/tex]
f · g = [tex]f( g( x ) )[/tex]
= [tex]f( 2x + 4 )[/tex]
= [tex]\sqrt{(2x + 4) - 3}[/tex]
= [tex]\sqrt{2x + 1}[/tex]
Since the g(x) is in the inside, that is what goes in first to produce the f(2x + 4). Now we put in (2x + 4) into the x of the f(x) function.
This produces: [tex]\sqrt{(2x + 4) - 3}[/tex]
Now, we just combine like terms to get: [tex]\sqrt{2x + 1}[/tex]
