Algebra Examples

$f (x) = x^{2} - 4 x + 6$ $g (x) = - 3 x + 1$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{2} - 4 x + 6)$ by substituting in the value of $f$ into $g$ .

$g (x^{2} - 4 x + 6) = - 3 (x^{2} - 4 x + 6) + 1$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (x^{2} - 4 x + 6) = - 3 x^{2} - 3 (- 4 x) - 3 \cdot 6 + 1$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $- 4$ by $- 3$ .

$g (x^{2} - 4 x + 6) = - 3 x^{2} + 12 x - 3 \cdot 6 + 1$

Step 3.2.2

Multiply $- 3$ by $6$ .

$g (x^{2} - 4 x + 6) = - 3 x^{2} + 12 x - 18 + 1$

Step 4

Add $- 18$ and $1$ .

$g (x^{2} - 4 x + 6) = - 3 x^{2} + 12 x - 17$