Solve for f f(x)=3(2)^x for x=-1

$f (x) = 3 {(2)}^{x}$ for $x = - 1$

Replace all occurrences of $x$ with $- 1$ in each equation.

Replace all occurrences of $x$ in $f (x) = 3 \cdot 2^{x}$ with $- 1$ .

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

$x = - 1$

Simplify $f (- 1) = 3 \cdot 2^{- 1}$ .

Simplify the left side.

Simplify $f (- 1)$ .

Move $- 1$ to the left of $f$ .

$- 1 f = 3 \cdot 2^{- 1}$

$x = - 1$

Rewrite $- 1 f$ as $- f$ .

$- f = 3 \cdot 2^{- 1}$

$x = - 1$

$- f = 3 \cdot 2^{- 1}$

$x = - 1$

$- f = 3 \cdot 2^{- 1}$

$x = - 1$

Simplify the right side.

Simplify $3 \cdot 2^{- 1}$ .

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- f = 3 \cdot \frac{1}{2}$

$x = - 1$

Combine $3$ and $\frac{1}{2}$ .

$- f = \frac{3}{2}$

$x = - 1$

$- f = \frac{3}{2}$

$x = - 1$

$- f = \frac{3}{2}$

$x = - 1$

$- f = \frac{3}{2}$

$x = - 1$

$- f = \frac{3}{2}$

$x = - 1$

The simplified system is the arbitrary solution of the original system of equations.

$f = - \frac{3}{2}$

$x = - 1$

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