Express the domain of f(x)= square root of (4-3x-x^2)?

Question

anonymous · Answer

$$f(x)=\sqrt{4-3x-x^2}$$
$$=\sqrt{(4+x )(1-x)}$$
What can't x be?
You know that the number inside the square root cannot be negative.

anonymous · Answer

What is the smallest x-value that DOES NOT make the number inside the square root sign a negative?

anonymous · Answer

You have the number 0 inside the square root sign but not less than that or else it will be a negative.

anonymous · Answer

I need to express the domain of f(x) =$$\sqrt{4-3x-x^2}$$ in interval notation? It's for calculus

anonymous · Answer

We're taking it step by step. You're after this right?
$$x>?$$

anonymous · Answer

We're taking it step by step here mate.

anonymous · Answer

What x value makes the whole term 0?

anonymous · Answer

@Jilian

anonymous · Answer

1 makes the whole term zero

anonymous · Answer

Good so x has to be greater than or equal to 1.

anonymous · Answer

$$x \ge1$$

anonymous · Answer

Do you understand these concepts of intervals now?

anonymous · Answer

If you go below 1 you will find yourself having a value less than 0 inside the square root which you don't want.

anonymous · Answer

Anything greater than one will make the solution non existing. I'm not clear on this interval notation however.

anonymous · Answer

less than one sorry

anonymous · Answer

My bad. I thought it was x-1 rather than 1-x

anonymous · Answer

Apologies.

anonymous · Answer

$$x \le1$$

anonymous · Answer

Now for the 4+x

anonymous · Answer

What's the maximum negative number you can put in their that won't make it negative. SO what number in there would make the value become zero?

anonymous · Answer

-4 makes ( 4+x) = 0

anonymous · Answer

Good work. so then x can't be less than -4. So then, x has to be greater than or equal to -4.
$$x\ge -4$$

anonymous · Answer

Now you have these two inequalties.
$$x\le 1$$
$$x\ge -4$$
Is x ranging between these two inequalities?

anonymous · Answer

so the domain will look like this,  $$-4\le x \le1$$

anonymous · Answer

You owned it. Well Done. Excellent work mate.

anonymous · Answer

Thank You very much for your help. It was a pleasure working with you. You should be a Math professor.

anonymous · Answer

Now worries mate, and hahah, nah, I don't think so.

anonymous · Answer

No worries*