To determine for which values of [tex]\( x \)[/tex] the rational expression [tex]\(\frac{x-7}{2x^2 - 32}\)[/tex] is undefined, we need to find the values of [tex]\( x \)[/tex] that make the denominator equal to zero.
Let's start by setting the denominator equal to zero and then solve for [tex]\( x \)[/tex]:
[tex]\[ 2x^2 - 32 = 0 \][/tex]
First, we can isolate [tex]\( x^2 \)[/tex] by adding 32 to both sides:
[tex]\[ 2x^2 = 32 \][/tex]
Next, divide both sides by 2 to simplify:
[tex]\[ x^2 = 16 \][/tex]
Now, we need to find the square roots of 16 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \pm \sqrt{16} \][/tex]
The square root of 16 is 4, so we get two solutions:
[tex]\[ x = 4 \][/tex]
[tex]\[ x = -4 \][/tex]
Therefore, the rational expression [tex]\(\frac{x-7}{2x^2 - 32}\)[/tex] is undefined for [tex]\( x = 4 \)[/tex] and [tex]\( x = -4 \)[/tex].
So, the correct values of [tex]\( x \)[/tex] for which the expression is undefined are:
- A. -4
- F. 4
