Finite Math Examples

$f (x) = e (e^{x - 2})$

Step 1

Multiply $e$ by $e^{x - 2}$ by adding the exponents.

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Step 1.1

Multiply $e$ by $e^{x - 2}$ .

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Step 1.1.1

Raise $e$ to the power of $1$ .

$f (x) = e e^{x - 2}$

Step 1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (x) = e^{1 + x - 2}$

Step 1.2

Subtract $2$ from $1$ .

$f (x) = e^{x - 1}$

Step 2

Find $f (- x)$ .

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Step 2.1

Find $f (- x)$ by substituting $- x$ for all occurrence of $x$ in $f (x)$ .

$f (- x) = e^{(- x) - 1}$

Step 2.2

Remove parentheses.

$f (- x) = e^{- x - 1}$

Step 3

A function is even if $f (- x) = f (x)$ .

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Step 3.1

Check if $f (- x) = f (x)$ .

Step 3.2

Since $e^{- x - 1}$ $\neq$ $e^{x - 1}$ , the function is not even.

The function is not even

Step 4

A function is odd if $f (- x) = - f (x)$ .

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Step 4.1

Multiply $- 1$ by $e^{x - 1}$ .

$- f (x) = - e^{x - 1}$

Step 4.2

Since $e^{- x - 1}$ $\neq$ $- e^{x - 1}$ , the function is not odd.

The function is not odd

Step 5

The function is neither odd nor even

Step 6