Question

determine whether the following equation defines y as a function of x.
x = 7y²
does the equation x = 7y² define y as a function of x?
∘ yes
∘ no
question help: video message instructor

Explanation:

Step1: Solve for y in terms of x

Start with the given equation:
$$x = 7y^2$$
Divide both sides by 7:
$$y^2 = \frac{x}{7}$$
Take square roots of both sides:
$$y = \pm\sqrt{\frac{x}{7}}$$

Step2: Apply function definition check

A function requires that each input $x$ (in the domain) maps to exactly one output $y$. For any positive $x$, the equation gives two distinct $y$-values: one positive and one negative.

Answer:

No