Question

Determine whether the equation$\sqrt{y}-x=5$ defines$\left(y\right)$ as a function of$\left(x\right)$.

Short answer

The given equation $\sqrt{y}-x=5$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 $\sqrt{y}-x=5$.

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

Solving the given equation,

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

Step 3. DESCRIPTION OF STEPS.

By simplifying the given equation, we obtain$y={\left(x+5\right)}^2$ 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 $f\left(x\right)={\left(x+5\right)}^2$.