Algebra Examples

$f (x) = 2 x^{2} - 5 x$ $g (x) = 3 x^{3}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (3 x^{3}) = 2 {(3 x^{3})}^{2} - 5 (3 x^{3})$

Step 3

Simplify each term.

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Step 3.1

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

$f (3 x^{3}) = 2 (3^{2} {(x^{3})}^{2}) - 5 (3 x^{3})$

Step 3.2

Raise $3$ to the power of $2$ .

$f (3 x^{3}) = 2 (9 {(x^{3})}^{2}) - 5 (3 x^{3})$

Step 3.3

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

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Step 3.3.1

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

$f (3 x^{3}) = 2 (9 x^{3 \cdot 2}) - 5 (3 x^{3})$

Step 3.3.2

Multiply $3$ by $2$ .

$f (3 x^{3}) = 2 (9 x^{6}) - 5 (3 x^{3})$

Step 3.4

Multiply $9$ by $2$ .

$f (3 x^{3}) = 18 x^{6} - 5 (3 x^{3})$

Step 3.5

Multiply $3$ by $- 5$ .

$f (3 x^{3}) = 18 x^{6} - 15 x^{3}$