How to find domain for f(x) = sqrt(25 - x^2)f(x)=√25−x2?

1 Answer
Rafael
Sep 29, 2015

[-5,5][−5,5]

Explanation:

So that the answer won't be imaginary, 25-x^225−x2 must be greater than or equal to 00.

{x|25-x^2>=0}{x∣25−x2≥0}
{x|25-x^2-25>=0-25}{x∣25−x2−25≥0−25}
{x|-x^2>=-25}{x∣−x2≥−25}
{x|(-1)(-x^2)<=(-1)(-25)}{x∣(−1)(−x2)≤(−1)(−25)}
{x|x^2<=25}{x∣x2≤25}

This will then be separated to two cases:
If xx is positive:
{x|x^2<=25}{x∣x2≤25}
{x|x<=5}{x∣x≤5}
color(blue)((-oo,5])(−∞,5]

If xx is negative:
{x|x^2<=25}{x∣x2≤25}
{x|x>=-5}{x∣x≥−5}
color(red)([-5,oo))[−5,∞)

We will then get the intersection of the two intervals:
color(blue)((-oo,5])nncolor(red)([-5,oo))(−∞,5]∩[−5,∞)
color(magenta)([-5,5][−5,5]

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