Calculus Examples

$f (x) = 3 x^{2} - 3$ ; $g (x) = \frac{8}{x}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{8}{x})$ by substituting in the value of $g$ into $f$ .

$f (\frac{8}{x}) = 3 {(\frac{8}{x})}^{2} - 3$

Step 3

Simplify each term.

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Step 3.1

Apply the product rule to $\frac{8}{x}$ .

$f (\frac{8}{x}) = 3 (\frac{8^{2}}{x^{2}}) - 3$

Step 3.2

Raise $8$ to the power of $2$ .

$f (\frac{8}{x}) = 3 (\frac{64}{x^{2}}) - 3$

Step 3.3

Multiply $3 \frac{64}{x^{2}}$ .

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Step 3.3.1

Combine $3$ and $\frac{64}{x^{2}}$ .

$f (\frac{8}{x}) = \frac{3 \cdot 64}{x^{2}} - 3$

Step 3.3.2

Multiply $3$ by $64$ .

$f (\frac{8}{x}) = \frac{192}{x^{2}} - 3$