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Sagot :
The domain of the function y = 2 - √(-3x+2) is (-∞ , 2/3] and the range of the function is (-∞ , 2] .
In the question ,
it is given that , the function is ⇒ y = 2- √(-3x+2) .
For Domain ,
we know that the square root function is defined only when the number inside the root is non negative .
that means ,
-3x [tex]+[/tex] 2 ≥ 0
Subtracting 2 from both the sides ,
we get ,
-3x ≥ -2
x ≤ 2/3
the Domain is (-∞ , 2/3] .
For range , we know that the root function value in always non negative .
√(-3x + 2) ≥ 0
Multiply by -1 on both sides
we get ,
-√(-3x + 2) ≤ 0
Adding 2 to both the sides
2 - √(-3x + 2) ≤ 2
y ≤ 2
the range is (-∞ , 2] .
Therefore , the domain is (-∞ , 2/3] and the range is (-∞ , 2] .
How do we find the domain and range of the function y = 2- √(-3x+2) ?
Learn more about Domain and Range here
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