Question

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

Short answer

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

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

Solving the given equation,

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

Step 3. DESCRIPTION OF STEPS.

By simplifying the given equation, we obtain$y^2=\frac{\pm \sqrt{2x-3}}{2}$ 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.