Q7. - Algebra 1

Question

State the excluded value for the function.

$\mathit{y}\mathbf{=}\frac{\mathbf{1}}{\mathbf{x}\mathbf{-}\mathbf{6}}$

Step-by-Step Solution

Answer

The excluded value for the function $y=\frac{1}{x-6}$ is $\mathit{x}\mathbf{=}\mathbf{6}$.

Step 1. Define a rational function.

A function of the form $y=\frac{p}{q}$ is called a rational function, where $p$ and $q$ are the polynomials and $q\ne 0$.

Step 2. Define the excluded values for the rational function.

Any value of a variable that results in a denominator of zero in a rational function is excluded from the domain of the function and these values are called the excluded values of the rational function.

Step 3. Calculate the excluded value for the function y = 1 x − 6 .

Observe the rational function $y=\frac{1}{x-6}$.

For excluded value,

Denominator $=0$

$\begin{array}{l}x-6=0\\ x=6\end{array}$

Therefore the excluded value for the function $y=\frac{1}{x-6}$ is $x=6$.