What is the domain of the function y=sqrt x+4

Domain: set of all numbers that can be inputted into a function

Since you cannot take the square root of a negative number, this means that x-4 CANNOT be negative. So it's either 0 or it's positive.

So.. x−4≥0

x−4+4≥0+4

x≥4

So this says: "Any number greater than or equal to 4 will result in x-4 being either 0 or some positive number"

So this means that the domain is

{x|x≥4}

This basically says: "the domain is the set of all numbers x such that x is greater than or equal to 4"

In interval notation, the domain is [4,∞)

The range is the set of all possible outputs. We can find the most extreme point of the range by plugging in the most extreme value for the domain

sqrt(x-4) = sqrt(4-4) = sqrt(0) = 0

So the smallest possible output is y=0, which means that the range is

{y|y≥0}

This basically says: "the range is the set of all numbers y such that y is greater than or equal to 0"

In interval notation, the range is

[0,∞)

1) the property is   ixi = a ⇔x = a   o x = -a

4(x-5)+3= 15⇒4x-20+3 = 15⇒4x-17= 15⇒4x = 15+17⇒4x = 32⇒x =32/4= 8

4(x-5) +3= -15⇒4x-20 +3 = -15⇒4x-17= -15⇒4x =-15+17⇒4x = 2⇒x =2/4= 1/2

the values are x =8 and x = 0,5