Question

Determine whether the equation$3x^2-y=5$ defines$\left(y\right)$ as a function of$\left(x\right)$.

Short answer

The given equation $3x^2-y=5$defines $\left(y\right)$ as a function of $\left(x\right)$.

Step-by-step solution

Step 1. Write down the given equation.

The given equation is $3x^2-y=5$.

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

Solving the given equation,

$$\begin{gathered} 3x^2-y=5....\left(\text{Given}\right) \\ \text{or,}-y=-3x^2+5 \\ y=3x^2-5....\left(\text{Multiplyby}\left(-1\right)\right) \end{gathered}$$

Step 3. DESCRIPTION OF STEPS.

By simplifying the given equation, we obtain $y=3x^2-5$from which it can be interpreted that for unique value of $\left(x\right)$there exists a unique $\left(y\right)$. There for the given equation represents $\left(y\right)$as a function of $\left(x\right)$, which can also be written in function form as.

$f\left(x\right)=3x^2-5$