Answer :
To find the value of [tex]\((f - g)(2)\)[/tex], let's break it down step-by-step.
### Step 1: Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 2 \)[/tex]
The function [tex]\( f(x) \)[/tex] is given by:
[tex]\[ f(x) = 3x^2 + 1 \][/tex]
Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[ f(2) = 3(2)^2 + 1 \][/tex]
[tex]\[ f(2) = 3(4) + 1 \][/tex]
[tex]\[ f(2) = 12 + 1 \][/tex]
[tex]\[ f(2) = 13 \][/tex]
### Step 2: Evaluate [tex]\( g(x) \)[/tex] at [tex]\( x = 2 \)[/tex]
The function [tex]\( g(x) \)[/tex] is given by:
[tex]\[ g(x) = 1 - x \][/tex]
Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[ g(2) = 1 - 2 \][/tex]
[tex]\[ g(2) = -1 \][/tex]
### Step 3: Calculate [tex]\((f - g)(2)\)[/tex]
Now, we need to find [tex]\((f - g)(2)\)[/tex], which means:
[tex]\[ (f - g)(2) = f(2) - g(2) \][/tex]
Using the values we found:
[tex]\[ (f - g)(2) = 13 - (-1) \][/tex]
[tex]\[ (f - g)(2) = 13 + 1 \][/tex]
[tex]\[ (f - g)(2) = 14 \][/tex]
Therefore, the value of [tex]\((f - g)(2)\)[/tex] is [tex]\( \boxed{14} \)[/tex].
### Step 1: Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 2 \)[/tex]
The function [tex]\( f(x) \)[/tex] is given by:
[tex]\[ f(x) = 3x^2 + 1 \][/tex]
Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[ f(2) = 3(2)^2 + 1 \][/tex]
[tex]\[ f(2) = 3(4) + 1 \][/tex]
[tex]\[ f(2) = 12 + 1 \][/tex]
[tex]\[ f(2) = 13 \][/tex]
### Step 2: Evaluate [tex]\( g(x) \)[/tex] at [tex]\( x = 2 \)[/tex]
The function [tex]\( g(x) \)[/tex] is given by:
[tex]\[ g(x) = 1 - x \][/tex]
Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[ g(2) = 1 - 2 \][/tex]
[tex]\[ g(2) = -1 \][/tex]
### Step 3: Calculate [tex]\((f - g)(2)\)[/tex]
Now, we need to find [tex]\((f - g)(2)\)[/tex], which means:
[tex]\[ (f - g)(2) = f(2) - g(2) \][/tex]
Using the values we found:
[tex]\[ (f - g)(2) = 13 - (-1) \][/tex]
[tex]\[ (f - g)(2) = 13 + 1 \][/tex]
[tex]\[ (f - g)(2) = 14 \][/tex]
Therefore, the value of [tex]\((f - g)(2)\)[/tex] is [tex]\( \boxed{14} \)[/tex].
