Question

what is the domain of the function?
f(x) square root of x+1 over (x+4)(x-6)

Answer 1

Answer:

[-1,6)U(6, ∞)

Step-by-step explanation:

$f(x) = \frac{\sqrt{x+1}}{(x+4)(x-6)}$

In functions that have a square root, the radicand (the inside of the root) has to be ≥0. Otherwise, you would be dealing with imaginary numbers.

So, in our function,

$x+1 \geq0\\x\geq-1$

We have two factors in our denominator. Note that you cannot divide by 0. So to find where x cannot be, we have to set the denominator to 0.

$(x+4)(x-6)=0\\x+4=0 \\x-6 = 0\\\\x=-4\\x=6$

X cannot be either -4 or 6.

So, x has to be greater than or equal to -1 and cannot equal -4 or 6.

x≥-1, x≠6