what is the domain of :the cubed root of (1-x)-1?
The cube root of a negative number is negative. Thus for large enough positive x you can have an arbitrarily large negative number and for large enough negative x, you can have an arbitrarily large positive number. The domain is therefore: ______
To determine the domain of the cubic root function, we need to consider the values of x that make the expression under the root defined.
In this case, the expression under the root is (1 - x) - 1.
To find the domain, we need to set this expression greater than or equal to zero since the cubic root function is defined for non-negative values.
(1 - x) - 1 ≥ 0
By simplifying, we get:
1 - x - 1 ≥ 0
-x ≥ -1
Multiplying both sides by -1 and flipping the inequality, we get:
x ≤ 1
Therefore, the domain of the cube root of (1 - x) - 1 is all real numbers less than or equal to 1.
To determine the domain of the function f(x) = ∛(1-x) - 1, we need to consider the restrictions on the values of x that make the function well-defined.
The first thing we need to consider is the denominator of the expression, which is (1-x). For the cubed root (∛) to be defined, the expression inside the root (1-x) must be greater than or equal to zero.
So, we set up the inequality: 1-x ≥ 0
Next, we solve the inequality:
1 ≥ x
This means that x must be less than or equal to 1.
Therefore, the domain of the function f(x) = ∛(1-x) - 1 is x ≤ 1.