Finite Math Examples

$f (x) = 10 x + 1$ , $g (x) = x^{2} + 10 x$ , $(f - g) (3)$

Step 1

Evaluate $f - g$ .

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Step 1.1

Replace the function designators in $f - g$ with the actual functions.

$(10 x + 1) - (x^{2} + 10 x)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$10 x + 1 - x^{2} - (10 x)$

Step 1.2.2

Multiply $10$ by $- 1$ .

$10 x + 1 - x^{2} - 10 x$

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Combine the opposite terms in $10 x + 1 - x^{2} - 10 x$ .

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Step 1.3.1.1

Subtract $10 x$ from $10 x$ .

$1 - x^{2} + 0$

Step 1.3.1.2

Add $1 - x^{2}$ and $0$ .

$1 - x^{2}$

Step 1.3.2

Reorder $1$ and $- x^{2}$ .

$- x^{2} + 1$

Step 2

Evaluate $f - g$ at $3$ .

$- {(3)}^{2} + 1$

Step 3

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

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Step 3.1

Remove parentheses.

$- {(3)}^{2} + 1$

Step 3.2

Simplify each term.

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Step 3.2.1

Raise $3$ to the power of $2$ .

$- 1 \cdot 9 + 1$

Step 3.2.2

Multiply $- 1$ by $9$ .

$- 9 + 1$

Step 3.3

Add $- 9$ and $1$ .

$- 8$