what are the modifications and x intercepts of the cubed root of (1-x)-1?
To find the modifications and x-intercepts of the cubic root of (1-x)-1, we first need to simplify the expression.
The given expression is: ³√((1-x)-1)
First, let's simplify the exponent part of the expression:
(1-x)-1 = 1/(1-x)
Now, let's substitute this simplified expression back into the original equation:
³√(1/(1-x))
Next, let's analyze the modifications and x-intercepts separately:
Modifications:
To determine the modifications, we need to look at the radicand (the expression under the radical symbol). In this case, the radicand is 1/(1-x).
For a cubic root, the value inside the root can be positive or negative, depending on the value of the expression. We need to find the conditions when the expression is positive or negative.
For 1/(1-x) to be positive, the denominator (1-x) has to be positive, and for 1/(1-x) to be negative, the denominator has to be negative.
When 1-x > 0 (1-x is positive), the modification is positive.
When 1-x < 0 (1-x is negative), the modification is negative.
X-intercepts:
To find the x-intercepts, we set the radicand (1/(1-x)) equal to zero and solve for x.
1/(1-x) = 0
For the fraction to be zero, the numerator must be zero, while the denominator cannot be zero.
1 = 0 * (1-x)
This equation is not possible since 1 is not equal to zero.
Therefore, there are no x-intercepts.
In summary:
- The modifications of the cubic root of (1-x)-1 are positive when 1-x > 0, and negative when 1-x < 0.
- There are no x-intercepts for the cubic root of (1-x)-1.