The domain means the values of x that make the equation untrue. So, we need to find the values that x cannot equal.
For square root functions, x cannot be a negative number. sqrt(-x) would give us isqrt(x), where i stands for imaginary number. We cannot represent i on graphs or within our domains. So, x must be larger than 0.
Can it equal 0 though? Well, let's change the square root to an exponential: sqrt0 = 0^(1/2). Now we have the "Zero Power Rule", which means 0, raised to any power, equals one. Thus, sqrt0=1. Ad one is within our rule of "must be greater than 0"
So, x can never bring the equation to take a square root of a negative number. So let's see what it would take to make the equation equal zero, and make that the edge of our domain!
To find the value of x the makes the expression equal to zero, let's set the problem equal to 0 and solve for x:
0= sqrt(7x+35)
square both sides
0^2 = cancelcolor(black)(sqrt(7x+35)^cancel(2)
0=7x+35
subtract 35 on both sides
-35=7x
divide by 7 on both sides
-35/7 = x
-5 = x
So, if x equals -5, our expression becomes sqrt0. That is the limit of our domain. Any smaller numbers than -5 would give us a square root of a negative number.
