What is the domain and range of these two problems?

Question

1. f(x) = ± square root of x

2. g(x) =9/3x−4

Answer 1

Remember, domain are the values of x and range are the values of f(x) or g(x) as the case may be.

1. The domain is non-negative real numbers. Or real numbers greater than or equal to zero. Negative real numbers return imaginary results. The range is all real numbers.

2. I assume you mean 9 / (3x - 4). The doman is x != 4/3. If x = 4/3, the denominator is zero, and the value is undefined. The range x != 0. The function can assume any other real value because it has asymptotes to +/- infinity as x approaches 4/3 from opposite sides. It also has an asymptote to 0 as x approaches +/- inifinity, but is never actually 0. (!= is read "bang equals," and is the same as the unequal sign or <>.)

Answer 2

1. domain: can't take the square root of a negative number (unless you want to work with complex numbers, which I'm assuming you don't). Therefore, the domain is: x >= 0.

range: for any real number y, you can find an x such that f(x) = y. If y >= 0, then x = y^2, and f(x) = f(y^2) = +sqrt(y^2) = y. If y<0, then let x = (-y)^2, and f(x) = f((-y)^2) = -sqrt((-y)^2) = y. So the range includes all real numbers.

I should point out that f is not a function; it's a relation, because there are two distinct y-values for every nonzero x-value. But the concepts of domain and range are still valid for a relation. Just like for a function, a domain consists of the first elements of all ordered pairs (x,f(x)) that belong to the relation, and the range consists of all second elements.

2. I assume you mean 9/(3x-4). You cannot divide by zero, so the domain consists of all x such that 3x-4 is nonzero. That is, all real numbers except 4/3.

For the range, let y = 9/(3x-4). Solve for x, and you get y(3x-4) = 9 => 3xy = 9 + 4y => x = (9+4y)/(3y). Because you cannot divide by zero, y cannot be zero, but for any other y, you can find an x for which g(x)=y, and that x is given by (9+4y)/(3y).

Answer 3

1. The domain can be any number 0 or greater. It can not be a negative unless you are dealing with imaginary numbers, and that would change the range as well.
The range is the set of all real numbers.

2. the domain is any real number other than 0 because you cannot divide by 0, I am assuming the denominator is 3x because if you meant 3x-4 it should be in ()
the range is the set of all real numbers.

Answer 4

The area potential that x may well be any huge style different than 0 because of the fact the sttement would not be actual if x have been 0 so which you area potential that x < 0 and x > 0 yet no longer equivalent to 0. the comparable is going for the style.

Answer 5

1) domain x>= 0 , range R
2) put () because i dont know what you mean with 9/3x : 9/(3x) i assume ...
domain : R\{0} ... means R except 0
Range : R

Answer 6

1.domain all real nos except negative numbers
range 0 to infinity
2.domain 3x-4>0
=>x>4/3
range all real numbers