Finite Math Examples

$f (x) = 2 \sqrt{- 2 x} - 3$

Step 1

Set the radicand in $\sqrt{- 2 x}$ less than $0$ to find where the expression is undefined.

$- 2 x < 0$

Step 2

Divide each term in $- 2 x < 0$ by $- 2$ and simplify.

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Step 2.1

Divide each term in $- 2 x < 0$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} > \frac{0}{- 2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} > \frac{0}{- 2}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x > \frac{0}{- 2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $- 2$ .

$x > 0$

Step 3

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x > 0$

$(0, \infty)$

Step 4