# How do you prove that g(x) = 1/2x is continuous at x=1/4?

Nov 25, 2017

#### Explanation:

To prove that the function $g \left(x\right) = \frac{1}{2} x$ is continuous at $x = \frac{1}{4} ,$ we

have to show that, ${\lim}_{x \to \frac{1}{4}} g \left(x\right) = g \left(\frac{1}{4}\right) .$

Now, ${\lim}_{x \to \frac{1}{x}} g \left(x\right) ,$

$= {\lim}_{x \to \frac{1}{4}} \frac{1}{2} x ,$

$= \frac{1}{2} \cdot \frac{1}{4} ,$

$= \frac{1}{8} ,$

$= g \left(\frac{1}{4}\right) .$

Hence, $g$ is continuous at $x = \frac{1}{4.}$