HELP!!! I got the first part done but I feel as though I did it wrong because I can't seem to get part 2 or 3 done.

Mathematics

2 answers:

Grace [21]3 years ago

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Sent a picture of the solution to the problem (s).

Stolb23 [73]3 years ago

6 0

Answer:

It's all below...

Step-by-step explanation:

Part 1.

quadratic poynomial function: f(x)=x2−5x+6

linear binomial: x−2

x−3x−2x2−5x+6x2−2x−−−−−−−−−−3x+6−3x+6−−−−−−−−0

Part 2.

f(2)=22−5(2)+6=4−10+6=−6+6=0

Part 3.

The remainder theorem says that if f(x) is divided by x-a, then f(a) will be the remainder. When we divided f(x) by x - 2 , we got a remainder of 0, which by the remainder theorem implies f(2) = 0. That means x-2 is a factor of f(x).

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Given f(x) = 2x - 2/4 the quantity of 2x minus 2 divided by 4, solve for f−1(3).

olga_2 [115]

The answer is that f-1(3) = 7.

In order to find the answer, we first must find the inverse function. The f-1 indicates that we are looking for an inverse. To find any inverse, we first must switch the x and f(x) values. We then solve for the new f(x), which gives us the inverse.

f(x) = (2x - 2)/4 ----> Switch x and f(x)

x = (2f(x) - 2)/4 -----> Multiply both sides by 4

4x = 2f(x) - 2 ----0-> Add 2 to both sides

4x + 2 = 2f(x) ------> Divide both sides by 2

f-1(x) = (4x + 2)/2

Now that we have the inverse function, we can put in 3 and find the answer.

f-1(x) = (4x + 2)/2

f-1(3) = (4(3) + 2)/2

f-1(3) = (12 + 2)/2

f-1(3) = (14)/2

f-1(3) = 7

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