We are given the following relation:

$\sqrt{1 - x} - 4y = 1$

Step 1: Isolate $y$

First, let's isolate $y$ by solving for $y$ in terms of $x$.

1. Start by moving the square root term to the other side of the equation: $-4y = 1 - \sqrt{1 - x}$
2. Now, divide both sides by $-4$ to solve for $y$: $y = \frac{1 - \sqrt{1 - x}}{-4}$ Simplifying the equation: $y = \frac{\sqrt{1 - x} - 1}{4}$

Thus, the relation rewritten as a function of $x$ is: $y = \frac{\sqrt{1 - x} - 1}{4}$

Would you like further details on this step or have any questions?

5 Related Questions:

1. How do we evaluate square root functions involving negative values?
2. Can we check if the function has any domain restrictions?
3. How would we find the inverse of this function?
4. What are some common transformations of the square root function?
5. How do you verify if a given function is one-to-one?

Tip:

When solving for a variable, remember to always check for possible restrictions in the domain, especially when dealing with square roots or fractions.