Simplify the expression for [tex]\( f(2) \)[/tex].

[tex]\[ f(2) = \frac{(2^2 - 2) \cdot 2^2 + 2 - 2}{2^2 + 2 - 6} \][/tex]



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]