Finite Math Examples

$f (x) = 21 x^{2}$ , $F (x) = a x^{3}$

Step 1

Set up the composite result function.

$f (F (x))$

Step 2

Evaluate $f (a x^{3})$ by substituting in the value of $F$ into $f$ .

$f (a x^{3}) = 21 {(a x^{3})}^{2}$

Step 3

Apply the product rule to $a x^{3}$ .

$f (a x^{3}) = 21 (a^{2} {(x^{3})}^{2})$

Step 4

Multiply the exponents in ${(x^{3})}^{2}$ .

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Step 4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$f (a x^{3}) = 21 (a^{2} x^{3 \cdot 2})$

Step 4.2

Multiply $3$ by $2$ .

$f (a x^{3}) = 21 (a^{2} x^{6})$

$f (a x^{3}) = 21 a^{2} x^{6}$