A rectangular box is constructed in 3-space with one corner at the origin and other vertices at (1, 0, 0), (0, 4, 0), (0, 0, 2).
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Answer:
B.
Step-by-step explanation:
According to the graph the function is defined for all real number except -3 and 7 (where the two red dashed vertical lines cross the x-axis)
so our function should be :
Since f(x) is a polynomial with 3rd degree, then it will have 3 roots (zeroes)
One of them is real and the other two are complex conjugate roots
Since the real root is 4, then
x = 4
Since the complex root is (1 - i), then
The other root will be the conjugate of it (1 + i)
x = (1 - i)
x = (1 + i)
To find f(x) we will multiply the three factors of it
We can get the factors from the zeroes
Subtract 4 from both sides
The first factor is (x - 4)
The second factor is (x - 1 + i)
The third factor is (x - 1 - i)
We will multiply them to find f(x)
Multiply it by (x - 4)
The answer is