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FrozenT [24]
3 years ago
15

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

Mathematics
1 answer:
Radda [10]3 years ago
5 0

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 <em>cannot </em>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

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