Precalculus Examples

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

Step 1

Set the radicand in $\sqrt{2 x - a}$ greater than or equal to $0$ to find where the expression is defined.

$2 x - a \geq 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $a$ to both sides of the inequality.

$2 x \geq a$

Step 2.2

Divide each term in $2 x \geq a$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 x \geq a$ by $2$ .

$\frac{2 x}{2} \geq \frac{a}{2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{a}{2}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{a}{2}$

Step 3

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$