For the synthetic division, you first put the coefficients on the right side. This rules out A and B. Then, you take the opposite of the bottom. So it says x+5, do it with -5, so the answer is C.
You need to take the whole function of g(x) and plug it into every single x within f(x). Bit tricky, so it just means we need to be careful. Alright, so this is the first set-up<span><span><span><span>−2x−7</span><span>x−1</span></span>−7</span><span><span><span>−2x−7</span><span>x−1</span></span>+2</span></span>So what You should do is make the top portion and the bottom portion all into one fraction. This means I need a common denominator. So to do this, I'll take x-1 as a common denominator and multiply it up into the numerator and the imaginary 1 denominator of -7 and 2. Doing this I have:<span><span><span>−2x−7−7(x−1)</span><span>x−1</span></span><span><span>−2x−7+2(x−1)</span><span>x−1</span></span></span>From here if I divide the top fraction and the bottom fraction, (x-1) will cancel out dueto me flipping the bottom fraction and multiplying. So that leaves me with:<span><span>−2x−7−7(x−1)</span><span>−2x−7+2(x−1)</span></span>Now if I multiply everything out and combine like terms I will have:<span><span><span>−2x−7−7x+7</span><span>−2x−7+2x−2</span></span>=<span><span>−9x</span><span>−9</span></span>=x</span>So that is the first part. We have to check both ways to confirm they are actually inverses of each other, though. Take a look at this part and see if you can make sense of what I did.
2x² + 5x + 2 = 9
2x² + 5x + 2 - 9 = 9 - 9
2x² + 5x - 7 = 0
x = <u>-5 +/- √(5² - 4(2)(-7))</u>
2(2)
x = <u>-5 +/- √(25 + 56)</u>
4
x = <u>-5 +/- √(81)
</u> 4<u>
</u>x = <u>-5 +/- 9
</u> 4
x = <u>-5 + 9</u> x = <u>-5 - 9</u>
4 4
x = <u>4</u> x = <u>-14</u>
4 4
x = 1 x = -3.5
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55,000,000 is the answer :D
