Question

Give the domain of y = √6 − x using set builder notation.

Answer 1

Given:

A function y = $\sqrt{6-x}$.

To find:

Domain of function in set builder form.

Solution:

Given,

y = $\sqrt{6-x}$

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 = $\sqrt{6-x}$ 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 = $\sqrt{6-x}$ = { x : x is less than 6 }

Hence, domain of given function in set builder form is { x : x is less than 6 }.