Finite Math Examples

$f (x) = 2 x + 1$ , $g (x) = \frac{2}{x + 4}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{2}{x + 4})$ by substituting in the value of $g$ into $f$ .

$f (\frac{2}{x + 4}) = 2 (\frac{2}{x + 4}) + 1$

Step 3

Multiply $2 (\frac{2}{x + 4})$ .

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Step 3.1

Combine $2$ and $\frac{2}{x + 4}$ .

$f (\frac{2}{x + 4}) = \frac{2 \cdot 2}{x + 4} + 1$

Step 3.2

Multiply $2$ by $2$ .

$f (\frac{2}{x + 4}) = \frac{4}{x + 4} + 1$

Step 4

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

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Add $4$ and $4$ .

$f (\frac{2}{x + 4}) = \frac{x + 8}{x + 4}$