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If [tex]\( f(x) = 3x^2 + 1 \)[/tex] and [tex]\( g(x) = 1 - x \)[/tex], what is the value of [tex]\( (f - g)(2) \)[/tex]?

A. 12
B. 14
C. 36
D. 38

Sagot :

GinnyAnsweridn
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].
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