Precalculus Examples

$f (x) = 3 x^{2}$ , $g (x) = x - \frac{2}{x}$ , findf $(g (2))$

Step 1

Replace the function designators in $g (2)$ with the actual functions.

$(x - \frac{2}{x}) (2)$

Step 2

Simplify $(x - \frac{2}{x}) (2)$ .

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Step 2.1

Remove parentheses.

$(x - \frac{2}{x}) (2)$

Step 2.2

Apply the distributive property.

$x \cdot 2 - \frac{2}{x} \cdot 2$

Step 2.3

Move $2$ to the left of $x$ .

$2 \cdot x - \frac{2}{x} \cdot 2$

Step 2.4

Multiply $- \frac{2}{x} \cdot 2$ .

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Step 2.4.1

Multiply $2$ by $- 1$ .

$2 \cdot x - 2 \frac{2}{x}$

Step 2.4.2

Combine $- 2$ and $\frac{2}{x}$ .

$2 \cdot x + \frac{- 2 \cdot 2}{x}$

Step 2.4.3

Multiply $- 2$ by $2$ .

$2 \cdot x + \frac{- 4}{x}$

Step 2.5

Move the negative in front of the fraction.

$2 x - \frac{4}{x}$