Find the domain of the following functions:
f (x) = 1/(x - 10)
f (x) = √(3x-12)
#1. Division by zero is undefined, so you need x≠10
#1 √x requires that x≥0, so you need 3x-12 ≥ 0
need solution
To find the domain of a function, we need to consider any values of x that would result in an undefined expression or violate any restrictions of the function.
1. For the function f(x) = 1/(x-10), the only restriction is that the denominator cannot be equal to zero since division by zero is undefined. So, we need to find the values of x that make x - 10 equal to zero and exclude them from the domain.
Setting x - 10 = 0, we find x = 10. Therefore, x = 10 is not included in the domain since it would make the denominator zero. So, the domain of f(x) = 1/(x-10) is all real numbers except x = 10.
Domain: (-∞, 10) U (10, +∞)
2. For the function f(x) = √(3x-12), the expression inside the square root must be non-negative since square roots of negative numbers are undefined in the real number system. So, we need to find the values of x that make 3x-12 non-negative.
Setting 3x-12 ≥ 0, we can solve for x:
3x ≥ 12
x ≥ 4
Therefore, the values of x must be greater than or equal to 4 to keep the expression inside the square root non-negative. So, the domain of f(x) = √(3x-12) is all real numbers greater than or equal to 4.
Domain: [4, +∞)