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Determine whether the function is continuous on the entire real number line. Explain your reasoning.

Determine Whether The Function Is Continuous On The Entire Real Number Line Explain Your Reasoning class=

Sagot :

So,

Given the function:

[tex]f(x)=\frac{4}{x^2-36}[/tex]

To check if the function is continuous in the entire number real line, we need to analyze the restrictions in the domain.

As you can notice, the denominator of a rational function can't be zero, so:

[tex]x^2-36\ne0[/tex]

We're going to find the values of x such that:

[tex]x^2-36=0[/tex]

This is:

[tex]\begin{gathered} x^2=36 \\ x=\pm6 \end{gathered}[/tex]

As you can see, "x" can't take the values of 6 and -6. If that happens, the function is not defined. Thus, the function is not continuous on the entire real number line.