Finite Math Examples

$f (x) = \frac{x}{x + 1}$ , $g (x) = \frac{18}{x}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{18}{x})$ by substituting in the value of $g$ into $f$ .

$f (\frac{18}{x}) = \frac{\frac{18}{x}}{(\frac{18}{x}) + 1}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{18}{x}) = \frac{18}{x} \cdot \frac{1}{\frac{18}{x} + 1}$

Step 4

Simplify the denominator.

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Step 4.1

Write $1$ as a fraction with a common denominator.

$f (\frac{18}{x}) = \frac{18}{x} \cdot \frac{1}{\frac{18}{x} + \frac{x}{x}}$

Step 4.2

Combine the numerators over the common denominator.

$f (\frac{18}{x}) = \frac{18}{x} \cdot \frac{1}{\frac{18 + x}{x}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{18}{x}) = \frac{18}{x} \cdot (1 (\frac{x}{18 + x}))$

Step 6

Multiply $\frac{x}{18 + x}$ by $1$ .

$f (\frac{18}{x}) = \frac{18}{x} \cdot \frac{x}{18 + x}$

Step 7

Cancel the common factor of $x$ .

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Step 7.1

Cancel the common factor.

$f (\frac{18}{x}) = \frac{18}{x} \cdot \frac{x}{18 + x}$

Step 7.2

Rewrite the expression.

$f (\frac{18}{x}) = 18 (\frac{1}{18 + x})$

Step 8

Combine $18$ and $\frac{1}{18 + x}$ .

$f (\frac{18}{x}) = \frac{18}{18 + x}$