To solve the problem, we need to evaluate the function [tex]\( g(x) = \sqrt{x - 3} \)[/tex] for the given values. Let's do this step-by-step.
### Step 1: Evaluate [tex]\( g(3) \)[/tex]
To find [tex]\( g(3) \)[/tex], we substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[ g(3) = \sqrt{3 - 3} = \sqrt{0} = 0 \][/tex]
### Step 2: Evaluate [tex]\( g(4) \)[/tex]
To find [tex]\( g(4) \)[/tex], we substitute [tex]\( x = 4 \)[/tex] into the function:
[tex]\[ g(4) = \sqrt{4 - 3} = \sqrt{1} = 1 \][/tex]
### Step 3: Evaluate [tex]\( g(x - 3) \)[/tex]
To find [tex]\( g(x - 3) \)[/tex], we substitute [tex]\( x - 3 \)[/tex] into the function:
[tex]\[ g(x - 3) = \sqrt{(x - 3) - 3} = \sqrt{x - 6} \][/tex]
### Summary
- [tex]\( g(3) = 0 \)[/tex]
- [tex]\( g(4) = 1 \)[/tex]
- [tex]\( g(x - 3) = \sqrt{x - 6} \)[/tex]
These are the values we obtain by evaluating the function [tex]\( g(x) \)[/tex] for the given arguments.
