Question

2. Given the domain of y = √2 - x using set builder notation.​

Answer 1

Step-by-step explanation:

For a real function, to exist, must have a real range.

f(x) = √2 - x, to be real, value under root must be 0 or greater than 0.

=> 2 - x ≥ 0

=> 2 ≥ x, x must be less than 2 or 2.

x can be -ve as well, being less than 2.

So,

Domain = {x : x is less than 2 or 2},

Domain = (-∞, 2]

Answer 2

Given:

A function y = √2 - x

To find :

Domain of a function in set builder form.

Solution:

Since the square root does not have a negative value,

So, Domain of y = √2 - x is all the values for which ,

2 - x ≥ 0

x - 2 ≤ 0

x ≤  2

So, x ∈ ( - ∞ , 2 )

To denote it in set builder form ,

Domain of y = { x : x is less than or equal to  2 }

Final answer:

The domain of a given function y = √2 - x using set builder notation is

{ x : x is less than or equal to 2 } .

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