Finite Math Examples

$f (n) = (f n - 2)$ , $f (0) = 1$ , $f (1) = - 1$

Step 1

Evaluate $f (0) = 1$ .

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Step 1.1

Evaluate $f (0)$ .

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Step 1.1.1

Replace the variable $n$ with $0$ in the expression.

$f (0) = f (0) - 2$

Step 1.1.2

Simplify $f (0) - 2$ .

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Step 1.1.2.1

Remove parentheses.

$f (0) - 2$

Step 1.1.2.2

Multiply $f$ by $0$ .

$0 - 2$

Step 1.1.2.3

Subtract $2$ from $0$ .

$- 2$

Step 1.2

Solve $- 2 = 1$ .

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Step 1.2.1

Since $- 2 \neq 1$ , there are no solutions.

No solution

Step 2

Evaluate $f (1) = - 1$ .

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Step 2.1

Evaluate $f (1)$ .

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Step 2.1.1

Replace the variable $n$ with $1$ in the expression.

$f (1) = f (1) - 2$

Step 2.1.2

Simplify $f (1) - 2$ .

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Step 2.1.2.1

Remove parentheses.

$f (1) - 2$

Step 2.1.2.2

Multiply $f$ by $1$ .

$f - 2$

Step 2.2

Solve $f - 2 = - 1$ .

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Step 2.2.1

Move all terms not containing $f$ to the right side of the equation.

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Step 2.2.1.1

Add $2$ to both sides of the equation.

$f = - 1 + 2$

Step 2.2.1.2

Add $- 1$ and $2$ .

$f = 1$

Step 3

List all of the solutions.

No solution