Mr. Altaffer goes to the pet store to buy a few treats for his puppy. He chooses one and then another. What is the probability t
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Answer:
Step-by-step explanation:
Remembert that, by definition:
→
Then, you can rewrite in exponential form:
Now you can solve for the variable "x":
Add 6 to both sides of the equation:
And finally you must divide both sides of the equation by 2, then:
It's clear that for x not equal to 4 this function is continuous. So the only question is what happens at 4.
<span>A function, f, is continuous at x = 4 if
</span><span>
</span><span>In notation we write respectively
</span>
Now the second of these is easy, because for x > 4, f(x) = cx + 20. Hence limit as x --> 4+ (i.e., from above, from the right) of f(x) is just <span>4c + 20.
</span>
On the other hand, for x < 4, f(x) = x^2 - c^2. Hence
Thus these two limits, the one from above and below are equal if and only if
4c + 20 = 16 - c²<span>
Or in other words, the limit as x --> 4 of f(x) exists if and only if
4c + 20 = 16 - c</span>²
That is to say, if c = -2, f(x) is continuous at x = 4.
Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers