Evaluate Using the Given Value f(5)=-2f(5-1)+3

$f (5) = - 2 f (5 - 1) + 3$

Step 1

Move $5$ to the left of $f$ .

$5 f = - 2 f (5 - 1) + 3$

Step 2

Simplify each term.

Subtract $1$ from $5$ .

$5 f = - 2 f \cdot 4 + 3$

Multiply $4$ by $- 2$ .

$5 f = - 8 f + 3$

Step 3

Move all terms containing $f$ to the left side of the equation.

Add $8 f$ to both sides of the equation.

$5 f + 8 f = 3$

Add $5 f$ and $8 f$ .

$13 f = 3$

Step 4

Divide each term in $13 f = 3$ by $13$ and simplify.

Divide each term in $13 f = 3$ by $13$ .

$\frac{13 f}{13} = \frac{3}{13}$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 f}{13} = \frac{3}{13}$

Divide $f$ by $1$ .

$f = \frac{3}{13}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$f = \frac{3}{13}$

Decimal Form:

$f = 0.\overline{230769}$