Precalculus Examples

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

Step 1

Replace the function designators in $f (x) - g x - h x$ with the actual functions.

$(3 x + 5) - (4 x^{2} - 2) - (x^{2} - 3 x + 1)$

Step 2

Simplify $(3 x + 5) - (4 x^{2} - 2) - (x^{2} - 3 x + 1)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$3 x + 5 - (4 x^{2}) - - 2 - (x^{2} - 3 x + 1)$

Step 2.1.2

Multiply $4$ by $- 1$ .

$3 x + 5 - 4 x^{2} - - 2 - (x^{2} - 3 x + 1)$

Step 2.1.3

Multiply $- 1$ by $- 2$ .

$3 x + 5 - 4 x^{2} + 2 - (x^{2} - 3 x + 1)$

Step 2.1.4

Apply the distributive property.

$3 x + 5 - 4 x^{2} + 2 - x^{2} - (- 3 x) - 1 \cdot 1$

Step 2.1.5

Simplify.

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Step 2.1.5.1

Multiply $- 3$ by $- 1$ .

$3 x + 5 - 4 x^{2} + 2 - x^{2} + 3 x - 1 \cdot 1$

Step 2.1.5.2

Multiply $- 1$ by $1$ .

$3 x + 5 - 4 x^{2} + 2 - x^{2} + 3 x - 1$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $3 x$ and $3 x$ .

$6 x + 5 - 4 x^{2} + 2 - x^{2} - 1$

Step 2.2.2

Add $5$ and $2$ .

$6 x - 4 x^{2} + 7 - x^{2} - 1$

Step 2.2.3

Subtract $x^{2}$ from $- 4 x^{2}$ .

$6 x - 5 x^{2} + 7 - 1$

Step 2.2.4

Simplify the expression.

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Step 2.2.4.1

Subtract $1$ from $7$ .

$6 x - 5 x^{2} + 6$

Step 2.2.4.2

Reorder $6 x$ and $- 5 x^{2}$ .

$- 5 x^{2} + 6 x + 6$