Find the domain of the function sqrt(4-x^2).
I tried it not sure if i'm correct
4-x^2>= 0
-x^2>=-4
x^2<=4
x<=2,x>=-2
Am I correct?
yes i totally. that is right
Yes, you are on the right track with solving for the domain of the function sqrt(4-x^2). Here's how you should approach it:
1. Start by setting the expression inside the square root, 4-x^2, greater than or equal to zero: 4-x^2 >= 0.
This is because the square root function is defined only for non-negative values.
2. Rearrange the inequality to isolate the squared term: -x^2 >= -4.
To do this, subtract 4 from both sides of the inequality.
3. Flip the inequality sign when multiplying or dividing by a negative number. Since the coefficient of x^2 is -1, we need to flip the inequality sign.
4. Divide both sides of the inequality by -1, remembering to flip the inequality sign: x^2 <= 4.
5. Take the square root of both sides of the inequality. Since we are dealing with a non-negative square root, you only need to consider the positive solution for x: x <= 2.
6. Finally, rewrite the domain using interval notation: (-∞, 2].
Therefore, the domain of the function sqrt(4-x^2) is (-∞, 2].