Precalculus Examples

What is $(f - g) (x)$ if $f (x) = 10 x + 4$ and $g (x) = 7 x + 4$ ?

Step 1

Evaluate $f - g$ .

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Step 1.1

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

$(10 x + 4) - (7 x + 4)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$10 x + 4 - (7 x) - 1 \cdot 4$

Step 1.2.2

Multiply $7$ by $- 1$ .

$10 x + 4 - 7 x - 1 \cdot 4$

Step 1.2.3

Multiply $- 1$ by $4$ .

$10 x + 4 - 7 x - 4$

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Combine the opposite terms in $10 x + 4 - 7 x - 4$ .

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Step 1.3.1.1

Subtract $4$ from $4$ .

$10 x - 7 x + 0$

Step 1.3.1.2

Add $10 x - 7 x$ and $0$ .

$10 x - 7 x$

Step 1.3.2

Subtract $7 x$ from $10 x$ .

$3 x$

Step 2

Evaluate $f - g$ at $x$ .

$3 (x)$

Step 3

Simplify $3 (x)$ .

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Step 3.1

Remove parentheses.

$3 (x)$

Step 3.2

Multiply $3$ by $x$ .

$3 x$