3. Give the domain of y= V6-* using set builder notation.give the solution
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3. Give the domain of y= V6-* using set builder notation.give the solution
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Given:
A function y = \sqrt{6-x}
6−x
.
To find:
Domain of function in set builder form.
Solution:
Given,
y = \sqrt{6-x}
6−x
Now, Set can be represented in roaster form or set builder form.
Set builder form: In this form a statement is written within {} so that set is defined completely.
Now,
Domain of y = \sqrt{6-x}
6−x
is all the values of for which,
6 - x \geq≥ 0
x -6 \leq≤ 0
x \leq≤ 6
so, x ∈ (-∞, 6 ]
Now, In set builder form,
Domain of y = \sqrt{6-x}
6−x
= { x : x is less than 6 }
Hence, domain of given function in set builder form is { x : x is less than 6 }.