State the domain of function, pa help po pls

Given:

The functions are:

(1)

(2)

(3)

To find:

The domain of given functions.

Solution:

Domain is the set of input and x -values.

Value under the square root must be positive because if the number under square root is negative, then it is a complex or imaginary number.

(1)

The function is defined if

The function is defined for all real values of x which are less than or equal to 1.

Therefore, the domain of the function is (-∞,1].

(2)

It is a linear function and linear function is defined for all real values of x.

Therefore, the domain of the function is (-∞,∞).

(3)

It can be written as

It is defined if

This function defined for all real values of x from -4 to 4.

Therefore, the domain of the function is [-4,4].

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.