Precalculus Examples

$f (x) = 3 x - 1$ , $g (x) = 2 x - x^{2}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (2 x - x^{2}) = 3 (2 x - x^{2}) - 1$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (2 x - x^{2}) = 3 (2 x) + 3 (- x^{2}) - 1$

Step 3.2

Multiply $2$ by $3$ .

$f (2 x - x^{2}) = 6 x + 3 (- x^{2}) - 1$

Step 3.3

Multiply $- 1$ by $3$ .

$f (2 x - x^{2}) = 6 x - 3 x^{2} - 1$

Step 4

Reorder $6 x$ and $- 3 x^{2}$ .

$f (2 x - x^{2}) = - 3 x^{2} + 6 x - 1$