Answer: The first option is correct.
Explanation:
The given piecewise function is,
From the piecewise function we can say that if x<0, then
If 
, then
Since the f(x) is defined for x<0 and , therefore the function f(x) is not defined for 
.
In the graph 2, 3 and 4 for each value of x there exist a unique value of y, therefore the function is defined for all values of x, which is not true according to the given piecewise function.
Only in figure the value of y not exist when x lies between 0 to 2, including 0. It means the function is not defined for , hence the first option is correct.
Answer:
x > -6
Step-by-step explanation:
Move 6 to the other side:
0.5x > -3
x > -6
Answer:
Solutions are 2, -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i
or 2, -1 + 1.58 i and -1 - 1.58i
(where the last 2 are equal to nearest hundredth).
Step-by-step explanation:
The real solution is x = 2:-
x^3 - 8 = 0
x^3 = 8
x = cube root of 8 = 2
Note that a cubic equation must have a total of 3 roots ( real and complex in this case). We can find the 2 complex roots by using the following identity:-
a^3 - b^3 = (a - b)(a^2 + ab + b^2).
Here a = x and b = 2 so we have
(x - 2)(x^2 + 2x + 4) = 0
To find the complex roots we solve x^2 + 2x + 4 = 0:-
Using the quadratic formula x = [-2 +/- sqrt(2^2 - 4*1*4)] / 2
= -1 +/- (sqrt( -10)) / 2
= -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i
