Explain how to determine which numbers must be excluded from the domain of a rational expression. Please provide an example with
1 answer:
Answer:
- When we are having a rational expression i.e. a expression of the type:
Where f(x) and g(x) are polynomial functions.
Now the domain of this rational expression is whole of the real numbers except the points where the function g(x) will be zero.
Hence we have to exclude the points where the given denominator quantity is zero.
- Let us consider an example as:
Let R(x) denote the rational function as:
Now the domain of this rational function will be whole of the real line minus the points where the denominator is zero.
We know that (x-2)(x-3) is zero when x=2 or x=3.
Hence, the domain of R(x) is: R- {2,3}.
You might be interested in
From the equation, it looks like we can set up a triangle like this. One side is x and the other is x + 20 because the northbound car traveled 20 miles farther. The hypotenuse is 100 because they were 100 miles apart.
Next, we can use the Pythagorean Theorem to solve for x:
a² + b² = c²
x² + (x + 20)² = 100²
This simplifies to:
x² + x² + 40x + 400 = 10000
2x² + 40x = 9600
2x² + 40x - 9600 = 0
After that, we can divided each side by 2:
x² + 20x - 4800 = 0
Next, we have to factor:
(x - 60)(x + 80) = 0
x = 60, -80
Since we know that distance can't be negative, 60 is the valid answer in this case.
x = 60
x + 20 = 80
Using this information, we know that the westbound car traveled 60 miles and the northbound car traveled 80 miles.
Next, we can use the Pythagorean Theorem to solve for x:
a² + b² = c²
x² + (x + 20)² = 100²
This simplifies to:
x² + x² + 40x + 400 = 10000
2x² + 40x = 9600
2x² + 40x - 9600 = 0
After that, we can divided each side by 2:
x² + 20x - 4800 = 0
Next, we have to factor:
(x - 60)(x + 80) = 0
x = 60, -80
Since we know that distance can't be negative, 60 is the valid answer in this case.
x = 60
x + 20 = 80
Using this information, we know that the westbound car traveled 60 miles and the northbound car traveled 80 miles.