Which ordered pair is on the inverse of f(x)? (–4, –2) (–2, –2) (–1, –2)
2 answers:
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When you see questions of this nature, test the individual inequalities and look out for their intersection.
For
Choose a point in the lower or upper half plane created by the line
The above line is the one which goes through the origin.
Now testing (1,0) yields,
That is,
This statement is true. So we shade the lower half of
For
We test for the origin because, it is not passing through the origin.
This yields
This statement is false so we shade the upper half.
The intersection is the region shaded in B. The top right graph
For
Choose a point in the lower or upper half plane created by the line
The above line is the one which goes through the origin.
Now testing (1,0) yields,
That is,
This statement is true. So we shade the lower half of
For
We test for the origin because, it is not passing through the origin.
This yields
This statement is false so we shade the upper half.
The intersection is the region shaded in B. The top right graph
So for this, we will be using synthetic division. To set it up, have the equation so that the divisor is -10 (since that is the solution of k + 10 = 0) and the dividend are the coefficients. Our equation will look as such:
<em>(Note that synthetic division can only be used when the divisor is a 1st degree binomial)</em>
- -10 | 1 + 2 - 82 - 28
- ---------------------------
Now firstly, drop the 1:
- -10 | 1 + 2 - 82 - 28
- ↓
- -------------------------
- 1
Next, you are going to multiply -10 and 1, and then combine the product with 2.
- -10 | 1 + 2 - 82 - 28
- ↓ - 10
- -------------------------
- 1 - 8
Next, multiply -10 and -8, then combine the product with -82:
- -10 | 1 + 2 - 82 - 28
- ↓ -10 + 80
- -------------------------
- 1 - 8 - 2
Next, multiply -10 and -2, then combine the product with -28:
- -10 | 1 + 2 - 82 - 28
- ↓ -10 + 80 + 20
- -------------------------
- 1 - 8 - 2 - 8
Now, since we know that the degree of the dividend is 3, this means that the degree of the quotient is 2. Using this, the first 3 terms are k^2, k, and the constant, or in this case k² - 8k - 2. Now what about the last coefficient -8? Well this is our remainder, and will be written as -8/(k + 10).
<u>Putting it together, the quotient is </u>