Precalculus Examples

f (x) = 2 x

$f (x) = 2 x$ ,

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

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

g (f (2))

$g (f (2))$

Step 1

Set up the composite result function.

g (f (x))

$g (f (x))$

Step 2

Evaluate

g (2 x)

$g (2 x)$ by substituting in the value of

f

$f$ into

g

$g$ .

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

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

Step 3

Evaluate the result function by replacing

x

$x$ with

2

$2$ in the function.

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

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

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)

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 5

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

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