Chapter 11, Problem 1CR

To determine

Choose the correct term to complete the sentence.

Answer to Problem 1CR

A value of x for which a rational function $f(x)$ is undefined at $a(n)$ is known as the excluded value.

Explanation of Solution

Given: A value of x for which a rational function $f(x)$ is undefined is $a(n)$ ? /.

Concept Used:

The denominator of any fraction cannot have the value zero. If the denominator of a fraction is zero, the expression is not a legal fraction because its overall value is undefined.

A rational expression is undefined when the denominator is equal to zero. To find the values that make a rational expression undefined, set the denominator equal to zero and solve the resulting equation. Example: $\frac{7x-4}{x-1}$ the function is undefined at x =1 Excluded value $x\ne 1$

In this question, such values of x are called excluded values, for example in the rational function $\frac{2}{x-3}$ , the excluded value is $x=3$ because at this the function is not defined

  $f(x)$ is undefined and an excluded value that $a(n)$ is for $\frac{a}{a(n)}$

Thus, a value of x for which a rational function $f(x)$ is undefined at $a(n)$ is known as the excluded value.