f(x) = x^2 + 2 g(x) = 2x^2 - 1
Find the domain of f+g, f-g, fg, and f/g
Can someone please explain to me how you would do this problem?
f,g,f+g,f-g,f*g all have domain of all reals, since they are just polynomials.
f/g has domain all reals except where g=0, that is, x=±1/√2
So for any set of polynomials that are not in a radical, the domain will usually be all real?
yes. They're just a bunch of powers of x. For any real value of x, you can find the function value.
Ok, that makes sense. Thank you!
I am doing a similar problem where f(x) and g(x) are both square root of x+5.
To find the domain of f+g and all that would I find the domain of each function...[-5,infinity). And then what? How would I add each set up?
To find the domain of a function, we need to determine the values of x for which the function is defined. This means we need to observe any restrictions or limitations on the domain.
Let's first find the domain for each operation separately:
1. Domain of f+g (addition):
To find the domain of f+g, we can add the two functions f(x) and g(x) together. Since both the functions f(x) and g(x) are defined for all real values of x, there are no restrictions on the domain. Therefore, the domain of f+g is all real numbers.
2. Domain of f-g (subtraction):
Similarly, since both f(x) and g(x) are defined for all real values of x, there are no restrictions on the domain of f-g as well. Therefore, the domain of f-g is all real numbers.
3. Domain of fg (multiplication):
To find the domain of fg, we need to consider any restrictions that might arise from the product of the two functions. Since both f(x) and g(x) are defined for all real values of x, there are no restrictions on the domain. Therefore, the domain of fg is all real numbers.
4. Domain of f/g (division):
To find the domain of f/g, we need to consider two things: first, since division by zero is undefined, we need to exclude any values of x that make the denominator zero. Second, since both f(x) and g(x) are defined for all real values of x except for the denominators becoming zero, there are no additional restrictions.
To find the values of x that make the denominator zero, we set g(x) = 0 and solve for x:
2x^2 - 1 = 0
2x^2 = 1
x^2 = 1/2
x = ±√(1/2)
x = ±(1/√2)
x = ±(√2/2)
So, the values of x that make the denominator zero are x = √(2/2) and x = -√(2/2), which simplify to x = 1/√2 and x = -1/√2.
Therefore, the domain of f/g is all real numbers except x = 1/√2 and x = -1/√2.
In summary:
- The domain of f+g is all real numbers.
- The domain of f-g is all real numbers.
- The domain of fg is all real numbers.
- The domain of f/g is all real numbers except x = 1/√2 and x = -1/√2.