Find the domain
(This in fraction form)
f(x)=x+3
x^2-4
f(x)= (This is in Radical:2-5x)
Any help, thank you!
My answers are:
(-infinity, 2) U (2, infinity0
(-infinity, 2/5)
agree
To find the domain of a function, we need to determine the values of x for which the function is valid and defined. In other words, we want to identify any values of x that might cause the function to be undefined or result in division by zero.
For the first function, f(x) = (x+3)/(x^2-4), we need to ensure that the denominator is not equal to zero. The denominator x^2-4 can be factored as (x-2)(x+2). Therefore, we should avoid values of x that make the denominator equal to zero, which are x = 2 and x = -2. Hence, the domain of the function is all real numbers except x = 2 and x = -2.
For the second function, f(x) = √(2-5x), we need to ensure that the expression inside the square root (√) is greater than or equal to zero. In other words, we need to find the values of x that make 2-5x greater than or equal to zero. Solving the inequality 2-5x ≥ 0, we get x ≤ 2/5. Hence, the domain of the function is all real numbers such that x ≤ 2/5.
So, the domain of the first function is all real numbers except x = 2 and x = -2, and the domain of the second function is all real numbers such that x ≤ 2/5.