What is the domain of the following function?
f(x) = √ -x + 2 - 1
You will have to use brackets to show where the square root ends
I suspect it is f(x) = √(-x+2) - 1 , or else why not combine the +2-1 ?
then the number under the square root must not be negative, that is ...
-x + 2 ≥ 0
-x ≥ -2
x ≤ 2
depends. How much of all that is under the radical sign?
Once you specify that, just remember that the domain of √u is u>=0.
To determine the domain of a function, we need to identify any values of x that would make the function undefined.
In this case, we have the function:
f(x) = √(-x + 2) - 1
The square root function (√) is defined for non-negative real numbers. Therefore, the expression inside the square root, -x + 2, must be greater than or equal to 0 for the function to have a real value.
To solve this inequality, we can isolate x:
-x + 2 ≥ 0
Adding x to both sides:
2 ≥ x
Rearranging the inequality:
x ≤ 2
So the domain of the function is all real numbers less than or equal to 2, or in interval notation, (-∞, 2].