which statement is true for g(x)? you can remove the discontinuity at x = 0 by defining g(0)=0. you can…

Explanation:

Step1: Recall continuity condition

A function is continuous at a point $x = a$ if $\lim_{x\rightarrow a}g(x)=g(a)$. We need to check the limit of $g(x)$ as $x$ approaches the points of discontinuity and see which re - definition makes the function continuous.

Step2: Analyze $x = 0$

As $x$ approaches $0$ from the left and right, the function values approach $0$. So, to remove the discontinuity at $x = 0$, we should define $g(0)=0$.

Step3: Analyze $x = 3$

As $x$ approaches $3$ from the left and right, the function values approach $- 1$. So, to remove the discontinuity at $x = 3$, we should define $g(3)=-1$.

Answer:

You can remove the discontinuity at $x = 3$ by defining $g(3)=-1$.