109k views
4 votes
Look in attachment ..answer if u know only pls

Look in attachment ..answer if u know only pls-example-1
User Samuraisam
by
7.7k points

1 Answer

6 votes
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
√(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 \ √(x) = √(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)


√(7x+22)


√(7(-3)+22)


√(1) =1
User Jezabel
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories