Question

Can someone explain to me why this function is continuous: g(x) = square root of 49 - x^2 on the interval (-7,7)

Answer 1

x^2 takes values from 0 till 49 on the above interval
So 49-x^2 takes values of 49 to 0 on the same interval
You have to take the square root of positive numbers, that does not cause a problem so the function is continuous.

Answer 2

Since the limits of the function g(x), from the left and from the right, are equal to the value of the function at the points x = -7 and x = 7