Chapter 6, Problem 1MCT

To determine

To find the value or values of the variable for which $\frac{9}{3x-2}$ is defined.

Answer to Problem 1MCT

The given expression is defined for all real values of $x$ except $x=\frac{2}{3}$.

Explanation of Solution

Given Information:

Given function: $\frac{9}{3x-2}$.

Concept Used:

The domain of the function is a set of input or argument values for which the function is defined.

Calculation:

Now, we know that the function $\frac{9}{3x-2}$ accept all values i.e. it takes all positive rational

Numbers as well as all negative rational numbers as input except $\left\{\frac{2}{3}\right\}$.

Since, we know that a division by the number zero is always undefined.

  $\begin{array}{l}\Rightarrow 3x-2\ne 0\\ \Rightarrow 3x\ne 2\\ \Rightarrow x\ne \frac{2}{3}\end{array}$

Hence, the maximum value that the function can take as input is $\infty$ whereas the minimum value that the function can take as input is $-\infty$.

So, domain of the function, $\frac{9}{3x-2}$ is $(-\infty ,\infty )~\left\{\frac{2}{3}\right\}$.