Help with Continuity - Did I do it right?

Question

1) Find the constant c that makes g continuous on (-infinity, infinity)
g(x) = {x^2-c^2 if x<4
{cx+20 if x>(less than or equal to)4
I got: by plugging in 4 into both equations
x^2-c^2=4^2-c^2=16-c^2 & cx+20=c(4)+20=4c+20
then combining them together: 4c+20=16-c^2
4c+4=-c^2
c^2+4c+4=0
(c+2)(c+2)=0
c+2=0
c+2=0
c=-2 & c=-2

2) Use the intermediate value theorem to prove that there is a positive number c such that c^2=2. (This proves the existence of the number sqrt[2])
c^2 is a polynomial & continuous function on its domain & its domain is from (-infinity, infinity)
It's an open interval so I took a closed interval of [1,2] from that open interval.
f(1)=1 & f(2)=4 so N=2 so there exists a number c in (1,2) such that f(c)=2

Answer 1

Yes, that's correct.

Answer 2

alright..bravo..u're doing great...

Answer 3

yep ur RIGHT