Precalculus Examples

$f (x) = 2 x$ , $g (x) = 3 x^{2} + 6$ , $g (f (2))$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (2 x)$ by substituting in the value of $f$ into $g$ .

$g (2 x) = 3 {(2 x)}^{2} + 6$

Step 3

Evaluate the result function by replacing $x$ with $2$ in the function.

$3 {(2 (2))}^{2} + 6$

Step 4

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 5