( 6x + 7 ) - ( -9x -9 ) simpilest form pls explain
1 answer:
You might be interested in
Answer: See attached table
Step-by-step explanation:
+---+---+---+
| 1 | 8 | 2 |
+---+---+---+
| 6 | 4 | 2 |
+---+---+---+
| 5 | 0 | 7 |
+---+---+---+
<u>Proofs:</u>
First row: 1+6+5 = 12
Second row: 8+4+0 = 12
Third row: 2+2+7 = 12
First column: 1+8+2 = 12
Second column: 6+4+2 = 12
Third column: 5+0+7 = 12
Diagonal starting from top left to bottom right: 1+4+7 = 12
Diagonal staring from top right to bottom left: 2+4+5 = 12
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