Chapter 9, Problem 4CR

To determine

The domain of the function $f\left(x\right)=\ln \left(1-2x\right)$ .

Answer to Problem 4CR

Solution:

The domain of the function $f\left(x\right)=\ln \left(1-2x\right)$ is $\left(-\infty ,\frac{1}{2}\right)$ .

Explanation of Solution

Given information:

The function is $f\left(x\right)=\ln \left(1-2x\right)$ .

Consider the function $f\left(x\right)=\ln \left(1-2x\right)$ .

The function $f\left(x\right)=\ln \left(1-2x\right)$ is logarithm function.

The logarithm function is defined only for positive real number.

The domain of $f\left(x\right)=\ln \left(1-2x\right)$ is all $x$ value such that $1-2x>0$ .

  $\Rightarrow 1>2x$

  $\Rightarrow \frac{1}{2}>x$

Hence, the domain of the function $f\left(x\right)=\ln \left(1-2x\right)$ is $\left\{x|\frac{1}{2}>x\right\}$ or equivalently $\left(-\infty ,\frac{1}{2}\right)$ .