Precalculus Examples

Find $(f - g) (2)$ if $f (x) = 4 x + 10$ and $g (x) = 3 x - 7$

Step 1

Evaluate $f - g$ .

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Step 1.1

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

$(4 x + 10) - (3 x - 7)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$4 x + 10 - (3 x) - - 7$

Step 1.2.2

Multiply $3$ by $- 1$ .

$4 x + 10 - 3 x - - 7$

Step 1.2.3

Multiply $- 1$ by $- 7$ .

$4 x + 10 - 3 x + 7$

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Subtract $3 x$ from $4 x$ .

$x + 10 + 7$

Step 1.3.2

Add $10$ and $7$ .

$x + 17$

Step 2

Evaluate $f - g$ at $2$ .

$(2) + 17$

Step 3

Simplify $(2) + 17$ .

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Step 3.1

Remove parentheses.

$(2) + 17$

Step 3.2

Add $2$ and $17$ .

$19$