Precalculus Examples

$f (x) = \frac{x}{\sqrt{1 - x^{2}}}$ , $f (3)$

Step 1

Replace the variable $x$ with $3$ in the expression.

$f (3) = \frac{3}{\sqrt{1 - {(3)}^{2}}}$

Step 2

Simplify $\frac{3}{\sqrt{1 - {(3)}^{2}}}$ .

Tap for more steps...

Step 2.1

Remove parentheses.

$\frac{3}{\sqrt{1 - {(3)}^{2}}}$

Step 2.2

Simplify the denominator.

Tap for more steps...

Step 2.2.1

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

$\frac{3}{\sqrt{1 - 1 \cdot 9}}$

Step 2.2.2

Multiply $- 1$ by $9$ .

$\frac{3}{\sqrt{1 - 9}}$

Step 2.2.3

Subtract $9$ from $1$ .

$\frac{3}{\sqrt{- 8}}$

Step 2.2.4

Rewrite $- 8$ as $- 1 (8)$ .

$\frac{3}{\sqrt{- 1 (8)}}$

Step 2.2.5

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$\frac{3}{\sqrt{- 1} \cdot \sqrt{8}}$

Step 2.2.6

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{3}{i \cdot \sqrt{8}}$

Step 2.2.7

Rewrite $8$ as $2^{2} \cdot 2$ .

Tap for more steps...

Step 2.2.7.1

Factor $4$ out of $8$ .

$\frac{3}{i \cdot \sqrt{4 (2)}}$

Step 2.2.7.2

Rewrite $4$ as $2^{2}$ .

$\frac{3}{i \cdot \sqrt{2^{2} \cdot 2}}$

Step 2.2.8

Pull terms out from under the radical.

$\frac{3}{i \cdot (2 \sqrt{2})}$

Step 2.2.9

Move $2$ to the left of $i$ .

$\frac{3}{2 i \sqrt{2}}$

Step 2.3

Multiply the numerator and denominator of $\frac{3}{2.82842712 i}$ by the conjugate of $2.82842712 i$ to make the denominator real.

$\frac{3}{2.82842712 i} \cdot \frac{i}{i}$

Step 2.4

Multiply.

Tap for more steps...

Step 2.4.1

Combine.

$\frac{3 i}{2.82842712 i i}$

Step 2.4.2

Simplify the denominator.

Tap for more steps...

Step 2.4.2.1

Add parentheses.

$\frac{3 i}{2.82842712 (i i)}$

Step 2.4.2.2

Raise $i$ to the power of $1$ .

$\frac{3 i}{2.82842712 (i^{1} i)}$

Step 2.4.2.3

Raise $i$ to the power of $1$ .

$\frac{3 i}{2.82842712 (i^{1} i^{1})}$

Step 2.4.2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 i}{2.82842712 i^{1 + 1}}$

Step 2.4.2.5

Add $1$ and $1$ .

$\frac{3 i}{2.82842712 i^{2}}$

Step 2.4.2.6

Rewrite $i^{2}$ as $- 1$ .

$\frac{3 i}{2.82842712 \cdot - 1}$

Step 2.5

Simplify the expression.

Tap for more steps...

Step 2.5.1

Multiply $2.82842712$ by $- 1$ .

$\frac{3 i}{- 2.82842712}$

Step 2.5.2

Move the negative in front of the fraction.

$- \frac{3 i}{2.82842712}$

Step 2.6

Factor $3$ out of $3 i$ .

$- \frac{3 (i)}{2.82842712}$

Step 2.7

Factor $2.82842712$ out of $2.82842712$ .

$- \frac{3 (i)}{2.82842712 (1)}$

Step 2.8

Separate fractions.

$- (\frac{3}{2.82842712} \cdot \frac{i}{1})$

Step 2.9

Divide $3$ by $2.82842712$ .

$- (1.06066017 \frac{i}{1})$

Step 2.10

Divide $i$ by $1$ .

$- (1.06066017 i)$

Step 2.11

Multiply $1.06066017$ by $- 1$ .

$- 1.06066017 i$