Find two functions defined implicitly by the given relation.
-$$x + y ^ { 2 } = 64$$
A) $y = \sqrt { 64 - x }$ or $y = \sqrt { 64 + x }$
B) $y = \sqrt { 64 - x }$ or $y = - \sqrt { 64 - x }$
C) $y = 64 - x$ or $y = 64 + x$
D) $y = 64 - x$ or $y = - 64 + x$

Question

Quizplus · Accepted Answer

Solving the given relation $x + y^2 = 64$ for $y$ gives two functions due to the square root operation: $y = \sqrt{64 - x}$ and $y = -\sqrt{64 - x}$, representing the positive and negative roots, respectively.

Find Two Functions Defined Implicitly by the Given Relation x+y2=64x + y ^ { 2 } = 64x+y2=64

Find Two Functions Defined Implicitly by the Given Relation $x + y ^ { 2 } = 64$