Answer :
Sure, I'll help you solve [tex]\( f(2) \)[/tex] step by step.
Let's rewrite the given function [tex]\( f(x) \)[/tex] at [tex]\( x = 2 \)[/tex]:
[tex]\[ f(2) = \frac{(2^2 - 2) \cdot 2^2 + 2 - 2}{2^2 + 2 - 6} \][/tex]
First, let's solve the expressions in the numerator and the denominator separately.
### Step 1: Simplify the Numerator
The numerator is given by:
[tex]\[ (2^2 - 2) \cdot 2^2 + 2 - 2 \][/tex]
1. [tex]\( 2^2 \)[/tex] means [tex]\( 2 \times 2 \)[/tex]:
[tex]\[ 2^2 = 4 \][/tex]
So,
[tex]\[ 2^2 - 2 = 4 - 2 = 2 \][/tex]
2. Now, multiply by [tex]\( 2^2 \)[/tex]:
[tex]\[ 2 \cdot 4 = 8 \][/tex]
3. Lastly, add the remaining terms:
[tex]\[ 8 + 2 - 2 = 8 \][/tex]
So the numerator simplifies to 8.
### Step 2: Simplify the Denominator
The denominator is given by:
[tex]\[ 2^2 + 2 - 6 \][/tex]
1. [tex]\( 2^2 = 4 \)[/tex] (as calculated before).
2. Now add 2 and subtract 6:
[tex]\[ 4 + 2 - 6 = 0 \][/tex]
So the denominator simplifies to 0.
### Step 3: Evaluate the Expression
Since we have:
- Numerator: 8
- Denominator: 0
We try to evaluate [tex]\( \frac{8}{0} \)[/tex]. However, in mathematics, division by zero is undefined. Therefore, the expression [tex]\( f(2) \)[/tex] is undefined.
### Conclusion
[tex]\[ f(2) \text{ is undefined because the denominator equals zero.} \][/tex]
Let's rewrite the given function [tex]\( f(x) \)[/tex] at [tex]\( x = 2 \)[/tex]:
[tex]\[ f(2) = \frac{(2^2 - 2) \cdot 2^2 + 2 - 2}{2^2 + 2 - 6} \][/tex]
First, let's solve the expressions in the numerator and the denominator separately.
### Step 1: Simplify the Numerator
The numerator is given by:
[tex]\[ (2^2 - 2) \cdot 2^2 + 2 - 2 \][/tex]
1. [tex]\( 2^2 \)[/tex] means [tex]\( 2 \times 2 \)[/tex]:
[tex]\[ 2^2 = 4 \][/tex]
So,
[tex]\[ 2^2 - 2 = 4 - 2 = 2 \][/tex]
2. Now, multiply by [tex]\( 2^2 \)[/tex]:
[tex]\[ 2 \cdot 4 = 8 \][/tex]
3. Lastly, add the remaining terms:
[tex]\[ 8 + 2 - 2 = 8 \][/tex]
So the numerator simplifies to 8.
### Step 2: Simplify the Denominator
The denominator is given by:
[tex]\[ 2^2 + 2 - 6 \][/tex]
1. [tex]\( 2^2 = 4 \)[/tex] (as calculated before).
2. Now add 2 and subtract 6:
[tex]\[ 4 + 2 - 6 = 0 \][/tex]
So the denominator simplifies to 0.
### Step 3: Evaluate the Expression
Since we have:
- Numerator: 8
- Denominator: 0
We try to evaluate [tex]\( \frac{8}{0} \)[/tex]. However, in mathematics, division by zero is undefined. Therefore, the expression [tex]\( f(2) \)[/tex] is undefined.
### Conclusion
[tex]\[ f(2) \text{ is undefined because the denominator equals zero.} \][/tex]
