Example:
This suggests two solutions,
and
.
However, upon plugging these solutions back into the equation, you get
which checks out, but
does not because
is defined only for
(assuming you're looking for real solutions only). So, we call
an extraneous solution, and the complete solution set (over the real numbers) is
.
Answer:
Domain: All Real Numbers
Range: All Real Numbers
Step-by-step explanation:
So the domain of a function can be defined as an interval of x-values, which you can input into the function and get real numbers as an output. Since we have a cube root here, or more specifically an odd nth root, the domain is all real numbers, since cbrt(negative number) will just be a negative number since (negative number * negative number * negative number) = negative number, so there does exist a solution, unlike even nth roots like square root, which is restricted to only positive values inside the radical, otherwise you get non-real solutions.
Now let's look at the range of the function, which can be defined as an interval of y-values which can possibly be outputted by the function.
Since as mentioned before, the cube root isn't limited to a certain interval, and rather all real numbers, the range is also similar, since whenever you have a negative number in the radical, the output will be a negative number, so the range is all real numbers
Answer:
y = 9
Step-by-step explanation:
1) Multiply both sides by 3.
3 × 3 = y
2) Simplfiy 3 × 3 to 9.
9 = y
3) Switch sides.
9
Answer: 
Step-by-step explanation:
To find the equation, you plug in the slope and given point. Then, you can solve and find the y-intercept.
[multiply]
[subtract both sides by 
]
Now that we have the y-intercept, the equation is .
