Question

Find the intervals on which the function is continuous.

y=1/|x|+2-x²/7
A. Continuous except at x=-7
B. Continuous except at x=-2
C. Continuous except at x=-7

Answer 1

The function y=1/|x|+2-x²/7 is continuous except at x=0 due to the absolute value term in the denominator.

Step-by-step explanation:

To find the intervals on which the function y = 1/|x| + 2 - x²/7 is continuous, we need to identify the values of x that could cause the function to be undefined or to have a jump or infinite discontinuity. The function has two components that can affect its continuity: the absolute value and the rational expression. The absolute value function, 1/|x|, is undefined at x = 0. Therefore, the function y has a discontinuity at x = 0. For the rational expression, we must check for points where the function could be undefined, which occurs when the denominator is zero. However, since x² and 7 are always positive, there are no values of x that make the second term undefined. Therefore, the only discontinuity in the function occurs at x = 0.