Q&A for How to Find the Domain of a Function

If your function is a fraction, set the denominator equal to 0 and solve. The domain would then be all real numbers except for whatever input makes your denominator equal to 0. For a square root, set whatever is inside the radical to greater than or equal to 0 and solve, since you can’t use any inputs that produce an imaginary number (i.e., the square root of a negative).

Yes. You can use a graphing calculator to calculate domain by plotting the function. There are also a variety of domain and range calculators online. Simply input your function to find the domain, which is a set of x-values that will successfully generate y-values.

The function tan(90x/2) is undefined at 90x/2 = pi/2 + pi*n, where n is an integer. Simply solve for x to obtain pi/90 + pi*n/45, where n is an integer.

There are no mathematical restrictions on those functions, but the economic context likely imposes an implied domain restriction. Probably x can't be negative or x must also be an integer (one can't sell half cars, for example).

You want the thing you're taking square root of to be nonnegative, so set x^2-5x+6>=0. Solve that for a domain of (-inf, 2] U [3, inf).

This site might have mangled your formatting, so apologies if I'm answering the wrong question. It looks like you're describing a function r which takes real numbers and outputs vectors. If so, then find the domain of each individual component of r. Then the domain of r is the intersection of the domains of each component. If each component is a polynomial like r(t) = 5t+1 or r(t) = t^2, then the domain is all of R.

Since sqrt(x) >= 0, the domain is [0,infinity), or all non-negative numbers.

The domain of y = 3x + 8 is all real numbers, since 3x is a linear function. Linear functions are polynomials, therefore having all real numbers.

You cannot divide by zero, so x^2 - 1000 != 0. Solve to get x = +- 10, so the domain is the real numbers except x = +-10.

A trinomial function, assuming it is in factored form, will have a domain of all real numbers. When you FOIL out the trinomials, you will get a resulting cubic function. Cubic functions are polynomials, therefore having a domain of all real numbers.

Since g is defined in terms of f, you need 2-x to be in the domain of f. The usual trick here is to check the endpoints of the domain, e.g. solve 2-x = -2 => x = 4, and 2-x = 3 => x = -1. Then check what happens on each interval. If x is less than -1, 2-x is too big; x=-1 doesn't work either because the domain of f is open on that side; but between -1 and 4 everything works; x=4 still works because the interval is closed on that side; and x greater than 4 is again outside the valid range. To summarize that in interval notation, write that the domain of g = (-1,4].

The domain is all values of x that don't cause the denominator of that fraction to equal zero (because you can't divide by zero). So let (3x - 7) = 0 and solve for x: 3x = 7, and x = 7/3. That means that the denominator is zero when x = 7/3. So the domain of f(x) is all real values of x except 7/3.

f(x)=5-2x, By definition, f is defined if and only if 5-2x is not equal to Zero. 5-2x=0, -2x=-5, x=5/2, Domain is all real numbers, except for 5/2.

It is the set of all real numbers, since every real number makes sense there.

The domain for this function is a set of all rel numbers. If you plot the graph of this function on a Cartesian plane, you will get function defined on the whole X-axis.

X^2+2^2>0 then x=(-2,2). Then Domain =(-2,2) 【OR】 X^2+4>0,Then subtract -4 on both sides X^2>-4 Then do √ing on both sides ,Then X=+2,-2.then Domain =(2,-2).

There are no restrictions to the value of x, because it is possible to input any x value into this equation and get a y value out. Therefore, the answer is (-inf,inf).

x^2 - 3x + 2 > 0. By Using quadratic equation. -b±√(b^2-4ac)/2a, we get; (-(-3)±√(-3)^2 - 4(1)(2))/2(1)=> (3±1)/2 =>4/2 ,. 2/2. => 2 ,. 1. Hence: D= (-infinity , 1] , [ 2 , infinity).

There is no function for finding the domain of a function. To find the domain, you must use differing rules depending on the function. For example, denominators can't be 0, square roots cannot be negative (apart from in the complex plane) and inverse exponential functions (logarithms) can't be taken of negative numbers or 0.

In this equation, there is only 1 pronumeral, x. Therefore, this is not a function but an equation. Technically, if you were to express it as a function, the domain would be the x input (-ln3-1), and the range the output (3).

In the Euclidian/Cartesian plane, negative square roots cannot be shown. Therefore, if you have a negative input into a sqrt function, there is no result, making the domain all values of x causing a natural number (including 0), or [0, infinity]) as the input into the sqrt. However, in the complex plane, the square roots of negative numbers fall across the y- (imaginary) axis, making the domain all negative numbers and 0, or [-infinity, 0].

To find the domain of a function, you must know what the function is, as each function has different rules about what x is, leave it undefined. Also, if the domain of the function is simply just -9, then that is your answer. Otherwise, saying the domain is -9 is incorrect. If you mean the size of the domain, then it doesn't make sense either, as they would have to be > or =0.

You cannot have a square root of numbers less than zero, so x+2> or =0. Therefore x> or = -2, making the domain [-2, infinity).

As explained above, when a function is a fraction, the domain (the possible values of x) includes all numbers except those that would result in a denominator of zero. In the function given here, the denominator would be zero if x is 7 or -7. So the domain is all numbers except +/-7.