Write as a Function of x square root of 1-x-2y=2

$\sqrt{1 - x} - 2 y = 2$

Step 1

Subtract $\sqrt{1 - x}$ from both sides of the equation.

$- 2 y = 2 - \sqrt{1 - x}$

Step 2

Divide each term in $- 2 y = 2 - \sqrt{1 - x}$ by $- 2$ and simplify.

Divide each term in $- 2 y = 2 - \sqrt{1 - x}$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{2}{- 2} + \frac{- \sqrt{1 - x}}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{2}{- 2} + \frac{- \sqrt{1 - x}}{- 2}$

Divide $y$ by $1$ .

$y = \frac{2}{- 2} + \frac{- \sqrt{1 - x}}{- 2}$

Simplify the right side.

Simplify each term.

Divide $2$ by $- 2$ .

$y = - 1 + \frac{- \sqrt{1 - x}}{- 2}$

Dividing two negative values results in a positive value.

$y = - 1 + \frac{\sqrt{1 - x}}{2}$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - 1 \cdot \frac{2}{2} + \frac{\sqrt{1 - x}}{2}$

Combine $- 1$ and $\frac{2}{2}$ .

$y = \frac{- 1 \cdot 2}{2} + \frac{\sqrt{1 - x}}{2}$

Combine the numerators over the common denominator.

$y = \frac{- 1 \cdot 2 + \sqrt{1 - x}}{2}$

Multiply $- 1$ by $2$ .

$y = \frac{- 2 + \sqrt{1 - x}}{2}$

Rewrite $- 2$ as $- 1 (2)$ .

$y = \frac{- 1 (2) + \sqrt{1 - x}}{2}$

Factor $- 1$ out of $\sqrt{1 - x}$ .

$y = \frac{- 1 (2) - 1 (- \sqrt{1 - x})}{2}$

Factor $- 1$ out of $- 1 (2) - 1 (- \sqrt{1 - x})$ .

$y = \frac{- 1 (2 - \sqrt{1 - x})}{2}$

Move the negative in front of the fraction.

$y = - \frac{2 - \sqrt{1 - x}}{2}$

Step 3

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = - \frac{2 - \sqrt{1 - x}}{2}$

Write as a Function of x square root of 1-x-2y=2

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