If h(x) is equal to ((x^2)-4)/(x+2) when x is not -2, and h(x) is continuous for all real numbers, then what is the value of h(-2)?
1. 0
2. -2
3. -4
4. 2
5. This is impossible. There is an infinite discontinuity at x=-2
To find the value of h(-2), we need to substitute -2 into the expression for h(x). However, we can see that the expression for h(x) is not defined when x is equal to -2 since division by zero is not allowed.
Given that h(x) is defined and continuous for all real numbers, we can conclude that option 5 is correct. There is an infinite discontinuity at x = -2, and therefore, it is not possible to determine the value of h(-2).
To find the value of h(-2), we need to substitute -2 into the function h(x).
Given that h(x) is ((x^2)-4)/(x+2) when x is not -2, we can directly substitute -2 into the function:
h(-2) = ((-2)^2) - 4) / (-2 + 2)
= (4 - 4) / 0
We cannot divide by zero, and the denominator of the expression becomes zero when x = -2. However, in the original statement, it is mentioned that h(x) is continuous for all real numbers.
Therefore, option 5 is correct: This is impossible. There is an infinite discontinuity at x = -2.
it is -4 just solve the limit and plug in -2
(x^2-4)/(x+2) = (x+2)(x-2)/(x+2) = x-2 when x is not -2.
At x = -2, f(x) is undefined.
So, if f(x) is defined to be -4 when x = -2 then the discontinuity is removed.