how do i know what the domain is in these problems...
i know that domain is the x value but how can i tell what it is?
y=1/x
y=3/x^2-49
y{x}
y=square root of 3-x
y=[x].
in plain English, the domain is the value of x that you may use in your given function to return a value
in your first one, remember that we cannot divide by zero, so x=0 is the only value which would not work
so the domain would be the set of real numbers, except x is not equal to zero
for your second, y = 3/(x^2-49)
the trouble arises when x = ± 7
do you think you can state the domain?
another case where difficulty arises is when your function tries to take the square root, (or any even root) of a negative number.
e.g. your third one:
y = √(3-x)
your domain would be all real values of x which would make (3-x) ≥ 0
i have a question.... when i get a function, how do i konw if it has an inverser... for example, y=ab.solute value x, then -2. i plugged in x=ab.solute val. of y, then -2. but how do i know if that is an inverse??
To determine the domain of a function, you need to analyze the restrictions on the input values (x) that would make the function undefined. Here are the specific cases for each of the functions you mentioned:
1. y = 1/x:
In this case, the function is undefined when the denominator (x) is equal to zero since dividing by zero is not possible. Therefore, for the domain of this function, you need to exclude the value x = 0. Hence, the domain would be all real numbers except for x = 0.
2. y = 3/(x^2 - 49):
Similar to the previous case, this function involves dividing by x^2 - 49. Dividing by zero is not allowed, so you need to identify the values of x that would make the denominator equal to zero. In this equation, the denominator is a difference of squares, x^2 - 49 = (x - 7)(x + 7). Hence, the function is undefined when x = 7 or x = -7. Therefore, the domain would be all real numbers except for x = 7 and x = -7.
3. y = √(3 - x):
For this function, the square root (√) is involved. Remember that the radicand, in this case, 3 - x, should not be negative. So, set the radicand greater than or equal to zero and solve for x: 3 - x ≥ 0. Rearranging the inequality, you get x ≤ 3. The domain of this function would be all real numbers x such that x is less than or equal to 3.
4. y = [x]:
In this case, the function represents the greatest integer function or the floor function. The domain is not restricted here since this function can handle all real numbers.
To summarize, always think about restrictions such as division by zero, square roots of negative numbers, or any other mathematical operations that might be undefined for certain values of x when determining the domain of a function.