Answer:
Option 3
Step-by-step explanation:
Given functions are,
f(x) = [tex]\frac{1}{x-3}[/tex]
g(x) = [tex]\sqrt{x+5}[/tex]
Therefore, composite function (f o g) will be,
(f o g)(x) = f[g(x)]
= [tex]\frac{1}{\sqrt{x+5} -3}[/tex]
This function will be defined for,
Denominator > 0
[tex]\sqrt{x+5}-3>0[/tex]
[tex]\sqrt{x+5} >3[/tex]
[tex](x+5)>3^2[/tex]
[tex]x+5>9[/tex]
[tex]x>9-5[/tex]
[tex]x>4[/tex]
And [tex]x+5\geq 0[/tex]
[tex]x\geq -5[/tex]
Therefore, domain of the composite function will be,
[-5, 4) ∪ (4, ∞)
Option 3 will be the answer.
