Precalculus Examples

$f^{- 1} (4) = 3$

Step 1

Divide each term in $f^{- 1} \cdot 4 = 3$ by $4$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $f^{- 1} \cdot 4 = 3$ by $4$ .

$\frac{f^{- 1} \cdot 4}{4} = \frac{3}{4}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Move $f^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4}{4 f} = \frac{3}{4}$

Step 1.2.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.2.2.1

Cancel the common factor.

$\frac{4}{4 f} = \frac{3}{4}$

Step 1.2.2.2

Rewrite the expression.

$\frac{1}{f} = \frac{3}{4}$

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$1 \cdot 4 = f \cdot 3$

Step 3

Solve the equation for $f$ .

Tap for more steps...

Step 3.1

Rewrite the equation as $f \cdot 3 = 1 \cdot 4$ .

$f \cdot 3 = 1 \cdot 4$

Step 3.2

Multiply $4$ by $1$ .

$f \cdot 3 = 4$

Step 3.3

Divide each term in $f \cdot 3 = 4$ by $3$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $f \cdot 3 = 4$ by $3$ .

$\frac{f \cdot 3}{3} = \frac{4}{3}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{f \cdot 3}{3} = \frac{4}{3}$

Step 3.3.2.1.2

Divide $f$ by $1$ .

$f = \frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$f = \frac{4}{3}$

Decimal Form:

$f = 1.\overline{3}$

Mixed Number Form:

$f = 1 \frac{1}{3}$