Question

The domain of the function $f\left(x\right)=\frac{x-4}{\sqrt{1-2x}}$ is

• A. $x\ne \frac{1}{2}$
• B. $x\ge 4$
• C. $x\ne 4$
• D. $x<\frac{1}{2}$
• E. $x>0$

Answer 1

The correct option is D $x<\frac{1}{2}$

Given, $f\left(x\right)=\frac{x-4}{\sqrt{1-2x}}$
We know that the term in square root should be always greater than zero.
So, we have $1-2x>0$ , which implies $x<\frac{1}{2}$
Therefore the domain is $x<\frac{1}{2}$