Algebra Examples

$f (x) = 3 x + 5$ $g (x) = 4 x^{2} - 2$ $h (x) = x^{2} - 3 x + 1$

Step 1

Set up the composite result function.

$f (h (x))$

Step 2

Evaluate $f (x^{2} - 3 x + 1)$ by substituting in the value of $h$ into $f$ .

$f (x^{2} - 3 x + 1) = 3 (x^{2} - 3 x + 1) + 5$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (x^{2} - 3 x + 1) = 3 x^{2} + 3 (- 3 x) + 3 \cdot 1 + 5$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $- 3$ by $3$ .

$f (x^{2} - 3 x + 1) = 3 x^{2} - 9 x + 3 \cdot 1 + 5$

Step 3.2.2

Multiply $3$ by $1$ .

$f (x^{2} - 3 x + 1) = 3 x^{2} - 9 x + 3 + 5$

Step 4

Add $3$ and $5$ .

$f (x^{2} - 3 x + 1) = 3 x^{2} - 9 x + 8$