Finite Math Examples

$f (x) = \frac{x + 4}{x^{2} - 16}$

Step 1

Simplify $f (x)$ .

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Step 1.1

Simplify the denominator.

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Step 1.1.1

Rewrite $16$ as $4^{2}$ .

$f (x) = \frac{x + 4}{x^{2} - 4^{2}}$

Step 1.1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 4$ .

$f (x) = \frac{x + 4}{(x + 4) (x - 4)}$

Step 1.2

Cancel the common factor of $x + 4$ .

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Step 1.2.1

Cancel the common factor.

$f (x) = \frac{x + 4}{(x + 4) (x - 4)}$

Step 1.2.2

Rewrite the expression.

$f (x) = \frac{1}{x - 4}$

Step 2

The word linear is used for a straight line. A linear function is a function of a straight line, which means that the degree of a linear function must be $0$ or $1$ . In this case, The degree of $f (x) = \frac{1}{x - 4}$ is $- 1$ , which makes the function a nonlinear function.

$f (x) = \frac{1}{x - 4}$ is not a linear function