Algebra Examples

$f (x) = 7 x^{2} + 5 x$ ; $g (x) = 3 x$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (3 x) = 7 {(3 x)}^{2} + 5 (3 x)$

Step 3

Simplify each term.

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Step 3.1

Apply the product rule to $3 x$ .

$f (3 x) = 7 (3^{2} x^{2}) + 5 (3 x)$

Step 3.2

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

$f (3 x) = 7 (9 x^{2}) + 5 (3 x)$

Step 3.3

Multiply $9$ by $7$ .

$f (3 x) = 63 x^{2} + 5 (3 x)$

Step 3.4

Multiply $3$ by $5$ .

$f (3 x) = 63 x^{2} + 15 x$