Precalculus Examples

If $f (x) = 6 x + 10$ and $g (x) = 7 x + 11$ ; what is $(g - f) (x)$ ?

Step 1

Evaluate $g - f$ .

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Step 1.1

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

$(7 x + 11) - (6 x + 10)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$7 x + 11 - (6 x) - 1 \cdot 10$

Step 1.2.2

Multiply $6$ by $- 1$ .

$7 x + 11 - 6 x - 1 \cdot 10$

Step 1.2.3

Multiply $- 1$ by $10$ .

$7 x + 11 - 6 x - 10$

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Subtract $6 x$ from $7 x$ .

$x + 11 - 10$

Step 1.3.2

Subtract $10$ from $11$ .

$x + 1$

Step 2

Evaluate $g - f$ at $x$ .

$(x) + 1$

Step 3

Simplify $(x) + 1$ .

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Step 3.1

Remove parentheses.

$(x) + 1$

Step 3.2

Remove parentheses.

$x + 1$