Question

Determine whether the equation$2x^2-4y^2=3$ defines$\left(y\right)$ as a function of$\left(x\right)$.

Short answer

The given equation $2x^2-4y^2=3$doesn’t define $\left(y\right)$ as a function of $\left(x\right)$.

Step-by-step solution

Step 1. Write down the given equation.

The given equation is $2x^2-4y^2=3$.

Step 2. Solve the given equation for (y) in terms of (x).

Solving the given equation,

$$\begin{gathered} 2x^2-4y^2=3....\left(\text{Given}\right) \\ \text{or,}4y^2=2x^2-3 \\ {y}^2=\frac{2x^2-3}{4} \\ y=\frac{\pm \sqrt{2x^2-3}}{2}\mathrm{....}\left(\text{Takesquareroot}\right) \end{gathered}$$

Step 3. Description of steps.

By simplifying the given equation, we obtain $y=\frac{\pm \sqrt{2x^2-3}}{2}$from which it can be interpreted that for unique value of $\left(x\right)$there exists two different values of $\left(y\right)$. Therefore the given equation cannot be written in function form.