Algebra Examples

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

Step 1

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

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Step 1.1

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

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

$x = - 1$

Step 1.2

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

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Step 1.2.1

Simplify the left side.

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Step 1.2.1.1

Simplify $f (- 1)$ .

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Step 1.2.1.1.1

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

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

$x = - 1$

Step 1.2.1.1.2

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

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

$x = - 1$

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

$x = - 1$

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

$x = - 1$

Step 1.2.2

Simplify the right side.

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Step 1.2.2.1

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

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Step 1.2.2.1.1

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

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

$x = - 1$

Step 1.2.2.1.2

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

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

$x = - 1$

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

$x = - 1$

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

$x = - 1$

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

$x = - 1$

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

$x = - 1$

Step 2

Reduce the system.

$f = - \frac{3}{2}, x = - 1$