Finite Math Examples

$f (1.2) = 1.1$ , $f (2) = 2$ , $f (4) = 4 + 4.2 \cdot \frac{1.3}{6}$

Step 1

Divide each term in $f (1.2) = 1.1$ by $1.2$ and simplify.

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Step 1.1

Divide each term in $f (1.2) = 1.1$ by $1.2$ .

$\frac{f \cdot 1.2}{1.2} = \frac{1.1}{1.2}$

$f (2) = 2$

$f (4) = 4.91$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $1.2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{f \cdot 1.2}{1.2} = \frac{1.1}{1.2}$

$f (2) = 2$

$f (4) = 4.91$

Step 1.2.1.2

Divide $f$ by $1$ .

$f = \frac{1.1}{1.2}$

$f (2) = 2$

$f (4) = 4.91$

$f = \frac{1.1}{1.2}$

$f (2) = 2$

$f (4) = 4.91$

$f = \frac{1.1}{1.2}$

$f (2) = 2$

$f (4) = 4.91$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $1.1$ by $1.2$ .

$f = 0.91\overline{6}$

$f (2) = 2$

$f (4) = 4.91$

$f = 0.91\overline{6}$

$f (2) = 2$

$f (4) = 4.91$

$f = 0.91\overline{6}$

$f (2) = 2$

$f (4) = 4.91$

Step 2

Replace all occurrences of $f$ with $0.91\overline{6}$ in each equation.

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Step 2.1

Replace all occurrences of $f$ in $f (2) = 2$ with $0.91\overline{6}$ .

$(0.91\overline{6}) (2) = 2$

$f = 0.91\overline{6}$

$f (4) = 4.91$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $0.91\overline{6}$ by $2$ .

$1.8\overline{3} = 2$

$f = 0.91\overline{6}$

$f (4) = 4.91$

$1.8\overline{3} = 2$

$f = 0.91\overline{6}$

$f (4) = 4.91$

Step 2.3

Replace all occurrences of $f$ in $f (4) = 4.91$ with $0.91\overline{6}$ .

$(0.91\overline{6}) (4) = 4.91$

$1.8\overline{3} = 2$

$f = 0.91\overline{6}$

Step 2.4

Simplify the left side.

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Step 2.4.1

Multiply $0.91\overline{6}$ by $4$ .

$3.\overline{6} = 4.91$

$1.8\overline{3} = 2$

$f = 0.91\overline{6}$

$3.\overline{6} = 4.91$

$1.8\overline{3} = 2$

$f = 0.91\overline{6}$

$3.\overline{6} = 4.91$

$1.8\overline{3} = 2$

$f = 0.91\overline{6}$

Step 3

Since $3.\overline{6} = 4.91$ is not true, there is no solution.

No solution

Step 4

Divide each term in $f (1.2) = 1.1$ by $1.2$ and simplify.

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Step 4.1

Divide each term in $f (1.2) = 1.1$ by $1.2$ .

$\frac{f \cdot 1.2}{1.2} = \frac{1.1}{1.2}$

$f (2) = 2$

$f (4) = 4.91$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $1.2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{f \cdot 1.2}{1.2} = \frac{1.1}{1.2}$

$f (2) = 2$

$f (4) = 4.91$

Step 4.2.1.2

Divide $f$ by $1$ .

$f = \frac{1.1}{1.2}$

$f (2) = 2$

$f (4) = 4.91$

$f = \frac{1.1}{1.2}$

$f (2) = 2$

$f (4) = 4.91$

$f = \frac{1.1}{1.2}$

$f (2) = 2$

$f (4) = 4.91$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $1.1$ by $1.2$ .

$f = 0.91\overline{6}$

$f (2) = 2$

$f (4) = 4.91$

$f = 0.91\overline{6}$

$f (2) = 2$

$f (4) = 4.91$

$f = 0.91\overline{6}$

$f (2) = 2$

$f (4) = 4.91$

Step 5

Replace all occurrences of $f$ with $0.91\overline{6}$ in each equation.

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Step 5.1

Replace all occurrences of $f$ in $f (2) = 2$ with $0.91\overline{6}$ .

$(0.91\overline{6}) (2) = 2$

$f = 0.91\overline{6}$

$f (4) = 4.91$

Step 5.2

Simplify the left side.

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Step 5.2.1

Multiply $0.91\overline{6}$ by $2$ .

$1.8\overline{3} = 2$

$f = 0.91\overline{6}$

$f (4) = 4.91$

$1.8\overline{3} = 2$

$f = 0.91\overline{6}$

$f (4) = 4.91$

Step 5.3

Replace all occurrences of $f$ in $f (4) = 4.91$ with $0.91\overline{6}$ .

$(0.91\overline{6}) (4) = 4.91$

$1.8\overline{3} = 2$

$f = 0.91\overline{6}$

Step 5.4

Simplify the left side.

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Step 5.4.1

Multiply $0.91\overline{6}$ by $4$ .

$3.\overline{6} = 4.91$

$1.8\overline{3} = 2$

$f = 0.91\overline{6}$

$3.\overline{6} = 4.91$

$1.8\overline{3} = 2$

$f = 0.91\overline{6}$

$3.\overline{6} = 4.91$

$1.8\overline{3} = 2$

$f = 0.91\overline{6}$

Step 6

Since $3.\overline{6} = 4.91$ is not true, there is no solution.

No solution