Question

Determine whether the equation defines y as a function of x x^2 + y^2 = 25

Answer 1

we are given

$x^2+y^2 =25$

We can solve for y

step-1: Subtract both sides by x^2

$x^2+y^2-x^2 =25-x^2$

$y^2 =25-x^2$

step-2: take sqrt both sides

$\sqrt{y^2} =\sqrt{25-x^2}$

$y =\sqrt{25-x^2}$

so, it is function on restricted intervals

so, we can get function as

$y =\sqrt{25-x^2}$

or

$y =-\sqrt{25-x^2}$..............Answer