Question

Find the restricted values of x. for the rational expression. If no restrictions, list no restrictions

Answer 1

To find the restricted values of x for a rational expression, we identify values that make the denominator zero by solving the associated quadratic equation using the quadratic formula. The calculated values are then checked for their relevance within the context of the problem.

Step-by-step explanation:

To find the restricted values of x for the rational expression, we need to identify any values that would make the denominator zero, which is undefined in mathematics. The question provided does not include the complete rational expression, but references an equation of the form x² + 0.0211x - 0.0211 = 0. This is a quadratic equation, and we can use the quadratic formula to find the possible values of x.

Firstly, we should check the expression for any denominators. Suppose we have an expression such as (1.00 - x) / (x² + 0.0211x - 0.0211). The denominator x² + 0.0211x - 0.0211 is the quadratic equation given to us. To find the restricted values of x, we look for values that would make the denominator zero.

Using the quadratic formula x = (-b ± √(b² - 4ac)) / (2a) where a, b, and c are coefficients from the quadratic equation ax² + bx + c = 0, we can calculate the potential values for x which cannot be used in the original expression, as they would make the denominator equal to zero. After applying the formula, we get two potential restricted values for x, which can be evaluated as:

x = 0.0216 or x = -0.0224

However, we must check which of these values are reasonable. If the context of the problem dictates that x must be within a certain range (like between 0 and 1), then we would discard any value that does not fall within that range.

Finally, it's important to eliminate terms wherever possible to simplify the algebra and check the answer to make sure it's reasonable.

Answer 2

In this rational expression, we need to find those values of x that can make the expression undefined. These values are those for which the denominator is equal to zero since a/0 is not defined. Then, we have:

`x^2+7=0`

Now, we need to find the values of x for which this expression is equal to zero:

1. Subtract 7 from both sides of the equation:

`x^2+7-7=0-7\Rightarrow x^2=-7\Rightarrow x=\pm\sqrt[]{-7}=x=\pm\sqrt[]{7i^2}`

We have values for complex roots. In this case, since we have this case, and the function must be in the set of the Real numbers, we can say that, in this function, we have no restrictions. In fact, if we graph the function, we have:

And we can see that the values for x are from -infinity to infinity (domain).