Let f(x)√3x and g(x) x+3 what the smallest number that is in the domain of fog

Question

i don't know what to do, I've tried so many things to figure it out and my parents don't even know what to do

 

 

Answer 1

You compose two functions:  f is composed of g(x).

 

(f o g)(x) = f(g(x)) = f(x + 3) = sqrt [3(x + 3)] = sqrt (3x + 9) 

 

Domain: {x | x >= 0} where x is the real number.  In other words, x is all real number where x is at least 0.

 

My suggestion is to graph the composed function in order to understand how domain works.  When you square root anything and plug in an input value, the output will not produce a negative number.

Answer 2

f(g(x)) =

 

f(x + 3) =

 

√(3(x + 3)) =

 

√(3x + 9)

 

 

Solve this inequality for x:

 

3x + 9 ≥ 0