Precalculus Examples

If $f (x) = 2 x$ and $g (x) = 2 x^{2} - 1$ find $f (g (3))$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (2 x^{2} - 1)$ by substituting in the value of $g$ into $f$ .

$f (2 x^{2} - 1) = 2 (2 x^{2} - 1)$

Step 3

Apply the distributive property.

$f (2 x^{2} - 1) = 2 (2 x^{2}) + 2 \cdot - 1$

Step 4

Multiply.

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Step 4.1

Multiply $2$ by $2$ .

$f (2 x^{2} - 1) = 4 x^{2} + 2 \cdot - 1$

Step 4.2

Multiply $2$ by $- 1$ .

$f (2 x^{2} - 1) = 4 x^{2} - 2$

Step 5

Evaluate the result function by replacing $x$ with $3$ in the function.

$4 {(3)}^{2} - 2$

Step 6

Simplify the evaluated function.

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Step 6.1

Simplify each term.

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Step 6.1.1

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

$4 \cdot 9 - 2$

Step 6.1.2

Multiply $4$ by $9$ .

$36 - 2$

Step 6.2

Subtract $2$ from $36$ .

$34$