Question

Determine where the function f(x) is continuous.
f(x) =√(x²-64)

Answer 1

The function f(x) = √(x²-64) is continuous for -8 ≤ x ≤ 8.

Step-by-step explanation:

To determine where the function f(x) = √(x²-64) is continuous, we need to look for any values of x that would make the function undefined. In this case, the function is defined as long as the expression inside the square root is greater than or equal to zero. So, x²-64 ≥ 0.

Solving this inequality, we get x ≥ -8 and x ≤ 8. Therefore, the function f(x) is continuous for -8 ≤ x ≤ 8.