To determine whether the function
[tex]\[
f(x) = \frac{x^2 + 4}{x^2}
\][/tex]
is defined at [tex]\(x = 0\)[/tex], we need to evaluate the function at this particular value of [tex]\(x\)[/tex].
1. Substitute [tex]\(x = 0\)[/tex] into the function:
[tex]\[
f(0) = \frac{0^2 + 4}{0^2}
\][/tex]
2. Simplify the expression inside the numerator and denominator:
[tex]\[
f(0) = \frac{4}{0}
\][/tex]
3. Interpret the result:
The expression [tex]\(\frac{4}{0}\)[/tex] is undefined in mathematics because division by zero is not defined. Therefore, the function [tex]\( f(x) \)[/tex] is undefined at [tex]\( x = 0 \)[/tex].
Hence, the function [tex]\( f(x) = \frac{x^2 + 4}{x^2} \)[/tex] is undefined at [tex]\( x = 0 \)[/tex].
