Let f(x) = 3x-7/x+1
Find the domain of f. Give your answer as an interval.
Thank you!
the way you typed it, the domain is the set of real numbers, x ≠ 0
What you probably meant is
f(x) = (3x-7)/(x+1)
In that case, the domain is the set of real numbers, x ≠ -1
To find the domain of f(x), we need to consider the values of x that make the expression valid. In this case, the expression involves division, so we need to exclude any values of x that would result in division by zero.
To find those values, we set the denominator equal to zero and solve for x.
x + 1 = 0
x = -1
Therefore, x = -1 is the value we need to exclude from the domain. Thus, the domain of f(x) is all real numbers except -1, so the domain can be expressed as:
(-∞, -1) U (-1, ∞)
This means that all real numbers except -1 are valid inputs for f(x).
To find the domain of a function, we need to identify any values that would result in undefined or undefined behavior. In this case, the only value that would cause a problem is if the denominator of the function is equal to zero since division by zero is undefined.
The denominator of the given function is x + 1. For division to be defined, x + 1 must not be zero. So, we solve the equation x + 1 = 0:
x + 1 = 0
x = -1
Therefore, the value -1 is not in the domain of the function since it would result in division by zero.
The domain of the function f(x) = 3x - 7 / (x + 1) is all real numbers except -1.
As an interval, we can represent the domain as (-∞, -1) U (-1, ∞).
So, the domain of f is (-∞, -1) U (-1, ∞).