Precalculus Examples

simplify composition of function $g (f (x))$ for $f (x) = - x + 1$ , $g (x) = 2 x - 5$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (- x + 1)$ by substituting in the value of $f$ into $g$ .

$g (- x + 1) = 2 (- x + 1) - 5$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (- x + 1) = 2 (- x) + 2 \cdot 1 - 5$

Step 3.2

Multiply $- 1$ by $2$ .

$g (- x + 1) = - 2 x + 2 \cdot 1 - 5$

Step 3.3

Multiply $2$ by $1$ .

$g (- x + 1) = - 2 x + 2 - 5$

Step 4

Subtract $5$ from $2$ .

$g (- x + 1) = - 2 x - 3$