Question

X² - 25

determine the intervals of continuity.
x² + 16
If the function is discontinuous at x = a, determine the type of discontinuity.
For the function f(x) =
O The function f is continuous on (-∞, -4) (-4, ∞o).
There is removable discontinuity at x = -4.
The function f is continuous on (-∞o, co).
The function f is continuous on (-∞o, 4) (4, 00).
There is removable discontinuity at x = 4.
O The function f is continuous on (-∞, -4) (-4, ∞0).
There is jump discontinuity at x = -4.

Answer 1

a)f(x) is defined for all real numbers, and the interval of continuity is (-∞, ∞)

b) The function f is continuous on (-∞, ∞).

How to determine interval of continuity of a function.

Given

f(x) = x² - 25/x² + 16

The function is defined everywhere except where the denominator is equal to zero because division by zero is undefined.

Therefore, we need to find where x² + 16 = 0

x² + 16 = 0

Solving for x

x² = -16

This has no real solutions, so the denominator is never equal to zero. Therefore, f(x) is defined for all real numbers, and the interval of continuity is (-∞, ∞)

b) Since the function is continuous over its entire domain, there is no discontinuity to consider, and the function has no points of discontinuity.

The function f is continuous on (-∞, ∞).