What is the doamin and range of:
y= square root of (3-2x)
The domain must be non-negative when we have a square root. Thus 3x-2 is greater than or equal to 0.
The range will be non-negative too.
All real y =>0. verify this.
To determine the domain and range of the function y = √(3 - 2x), let's start with the domain.
For a square root function, the value inside the square root (i.e., 3 - 2x) must be greater than or equal to zero. So we can set up the inequality:
3 - 2x ≥ 0
To solve this inequality, we need to isolate x:
-2x ≥ -3
Dividing both sides of the inequality by -2 (and flipping the inequality sign):
x ≤ 3/2
So the domain of the function is all values of x such that x is less than or equal to 3/2, or in interval notation: (-∞, 3/2].
Now, let's determine the range.
Since we have a square root function, the range will be all non-negative values (i.e., all real numbers greater than or equal to zero).
So the range of the function is [0, +∞).
To summarize:
Domain: (-∞, 3/2]
Range: [0, +∞)