Question

Look in attachment ..answer if u know only pls

Answer 1

First of all, you have to understand $g$ is a square-root function. 

Square-root functions are continuous across their entire domain, and their domain is all real x-values for which the expression within the square-root is non-negative. 

In other words, for any square-root function $q$ and any input $c$ in the domain of $q$ (except for its endpoint), we know that this equality holds:  $lim \ q(x)=q(c)$ 

Let's take $\sqrt{x}$ as an example. 

The domain of $\sqrt x$ is all real numbers such that $x \geq 0$.  Since $x=0$  is the endpoint of the domain, the two-sided limit at that point doesn't exist (you can't approach $0$ from the left). 

However, continuity at an endpoint only demands that the one-sided limit is equal to the function's value: 

$lim \ \sqrt{x} = \sqrt{0} =0$ 

In conclusion, the equality $lim \ q(x)=q(c)$ holds for any square-root function $q$ and any real number $c$  in the domain of $q$ except for its endpoint, where the two-sided limit should be replaced with a one-sided limit. 

The input $x=-3$,  is within the domain of $g$. 

Therefore, in order to find  $lim \ g(x)$  we can simply evaluate $g$ at $x-3$. 

$g(x)$ 

$\sqrt{7x+22}$ 

$\sqrt{7(-3)+22}$ 

$\sqrt{1} =1$