Calculus Examples

$f (x) = 2 x - 6$ , $g (x) = x^{2} + 9$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x^{2} + 9)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (x^{2} + 9) = 2 x^{2} + 2 \cdot 9 - 6$

Step 3.2

Multiply $2$ by $9$ .

$f (x^{2} + 9) = 2 x^{2} + 18 - 6$

Step 4

Subtract $6$ from $18$ .

$f (x^{2} + 9) = 2 x^{2} + 12$