if f(x) = sqrt(9-3x) determine the domain of f
To determine the domain of the function f(x) = sqrt(9-3x), we need to find the values of x for which the function is defined.
The square root function (√) is defined only for non-negative values. This means that the expression inside the square root (9-3x) must be greater than or equal to zero.
Therefore, we can set up the inequality:
9 - 3x ≥ 0
Now let's solve for x:
Subtract 9 from both sides of the inequality:
-3x ≥ -9
Divide both sides of the inequality by -3. Remember to reverse the direction of the inequality when dividing by a negative number:
x ≤ -9/-3
Simplifying:
x ≤ 3
Therefore, the domain of the function f(x) = sqrt(9-3x) is x ≤ 3. In other words, any value of x that is less than or equal to 3 will make the function defined.