Question

Consider the function $f(x)=\frac{x-2}{x^{2}-81}$. For what value of $x$, if any, will this function a) equal 0 ? b) be undefined? Explain.

Name: Problem 108, Chapter 6: Intermediate Algebra for College Students
Uploaded: 2019-07-12T13:47:45-08:00
Duration: 1 min 54 s
Channel: Yifan Xu
Description: Consider the function f(x)=(x-2)/(x^2-81). For what value of x, if any, will this function a) equal 0 ? b) be undefined? Explain.

   Consider the function $f(x)=\frac{x-2}{x^{2}-81}$. For what value of $x$, if any, will this function a) equal 0 ? b) be undefined? Explain.

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 6, Problem 108

Instant Answer

Solved by Expert Yifan Xu

07/12/2019

Step 1

So, we need to find the value of x that makes x-2 = 0. x - 2 = 0 x = 2 So, the function equals 0 when x = 2. Show more…

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Consider the function $f(x)=\frac{x-2}{x^{2}-81}$. For what value of $x$, if any, will this function a) equal 0 ? b) be undefined? Explain.

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Key Concepts

Rational Function

A rational function is defined as the ratio of two polynomials. Its behavior is significantly determined by the numerator and the denominator since the function is only defined when the denominator is nonzero.

Zeros of a Function

The zeros of a function are the values of the variable that make the function equal to zero. In the context of a rational function, this happens when the numerator is zero while the denominator remains nonzero.

Domain Restrictions

Domain restrictions in rational functions occur when the denominator equals zero, since division by zero is undefined. Identifying these values is essential to understanding where the function is not valid.

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