Finite Math Examples

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

Step 1

Set $\sqrt{x} - 3$ equal to $0$ .

$\sqrt{x} - 3 = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Add $3$ to both sides of the equation.

$\sqrt{x} = 3$

Step 2.2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{x}}^{2} = 3^{2}$

Step 2.3

Simplify each side of the equation.

Tap for more steps...

Step 2.3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(x^{\frac{1}{2}})}^{2} = 3^{2}$

Step 2.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.1

Simplify ${(x^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.3.2.1.1

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.3.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 2.3.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.2.1.1.2.1

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 2.3.2.1.1.2.2

Rewrite the expression.

$x^{1} = 3^{2}$

Step 2.3.2.1.2

Simplify.

$x = 3^{2}$

Step 2.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.1

Raise $3$ to the power of $2$ .

$x = 9$

Step 3