State the domain for f(x) =x/x+4 and y=√13+x and P(x) = −2^2 + 40x − 34

Question

state the domain

 

13+x is to the root did not show in question

Answer 1

f(x) = x/(x+4)  Yes you need parentheses; otherwise it's x/x + 4 = 1 + 4 = 5.  You can't divide by zero, so we cannot have x+4 = 0.  Thus x = -4 is excluded from the domain.  All other values of x are included.

 

y = √(13+x).  You can't take the square root of negative numbers, so we must have 13+x ≥ 0, so the domain is x ≥ -13.

 

P(x) = -2x² + 40x -34.  I added the x², which I think you intended to put into the problem but left out.  This is a quadratic equation.  The domain is all real numbers.