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Determine whether the function is defined at [tex]\( x = 0 \)[/tex]:

[tex]\[ f(x) = \frac{x^2 + 4}{x^2} \][/tex]

Sagot :

GinnyAnswer
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].
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