a) this is in the form y=mx+b so is a line and is therefore deifened for all values of x.
b)-1/(x2+2x-3) is a rational function, or a fraction. When dealing with a fraction, the denominator cannot be 0.
This means that x2+2x - 3 cannot equal 0.
(x+3)(x-1) cannot = 0
x cannot equal -3 and x cannot = 1.
c) with radical equations, the expression underneath the square root sign must be greater than or equal to 0 since the square root of negative numbers lead to imaginary numbers.
So, x-6 >=0 leads to x>=6.
Hope this helped.