Answer:
x = -2, x = 3 − i√8, and x = 3 + i√8
Step-by-step explanation:
g(x) = x³ − 4x² − x + 22
This is a cubic equation, so it must have either 1 or 3 real roots.
Using rational root theorem, we can check if any of those real roots are rational. Possible rational roots are ±1, ±2, ±11, and ±22.
g(-1) = 18
g(1) = 18
g(-2) = 0
g(2) = 12
g(-11) = 1782
g(11) = 858
g(-22) = -12540
g(22) = 8712
We know -2 is a root. The other two roots are irrational. To find them, we must find the other factor of g(x). We can do this using long division, or we can factor using grouping.
g(x) = x³ − 4x² − 12x + 11x + 22
g(x) = x (x² − 4x − 12) + 11 (x + 2)
g(x) = x (x − 6) (x + 2) + 11 (x + 2)
g(x) = (x (x − 6) + 11) (x + 2)
g(x) = (x² − 6x + 11) (x + 2)
x² − 6x + 11 = 0
Quadratic formula:
x = [ 6 ± √(36 − 4(1)(11)) ] / 2
x = (6 ± 2i√8) / 2
x = 3 ± i√8
The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.
Answer:
sorry I don't know
Step-by-step explanation:
sorry
Answer:
Invertible functions
Step-by-step explanation:
An inverse of a function is one that reverses the operation of the function such that the result of the function on a variable, is reversed back to the initial variable
Therefore, when we have the the result of the function, f on x as y given as follows;
f(x) = y
The inverse of the function, g on the result, y gives the initial variable, x as follows;
g(y) = x
Example of invertible functions includes;
f(x) = x²
An example of a non-invertible function includes;
f(x) = 2·x².
43 < y - 30
add 30 to both sides
73 < y
y can be anything that is greater than 73
so it could be...
101, 74, 90, 75, 980767, 5674, etc.
Hope this helps!
Answer:Her Aunt paid her 4.50 and hour and her neighbor 6 an hour. The difference is 1.5
Step-by-step explanation:
