Precalculus Examples

If $f (x) = \frac{1}{x}$ and $g (x) = 3 x + 2$ find $((f \circ g)) (2)$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (3 x + 2)$ by substituting in the value of $g$ into $f$ .

$f (3 x + 2) = \frac{1}{3 x + 2}$

Step 3

Evaluate the result function by replacing $x$ with $2$ in the function.

$\frac{1}{3 (2) + 2}$

Step 4

Simplify the denominator.

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Step 4.1

Multiply $3$ by $2$ .

$\frac{1}{6 + 2}$

Step 4.2

Add $6$ and $2$ .

$\frac{1}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$