Precalculus Examples

If $f (x) = x^{2} + 5 x$ and $g (x) = 7 - x$ ; find: $(f - g) (- 6)$

Step 1

Evaluate $f - g$ .

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Step 1.1

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

$(x^{2} + 5 x) - (7 - x)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$x^{2} + 5 x - 1 \cdot 7 - - x$

Step 1.2.2

Multiply $- 1$ by $7$ .

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

Step 1.2.3

Multiply $- - x$ .

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Step 1.2.3.1

Multiply $- 1$ by $- 1$ .

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

Step 1.2.3.2

Multiply $x$ by $1$ .

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

Step 1.3

Add $5 x$ and $x$ .

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

Step 2

Evaluate $f - g$ at $- 6$ .

${(- 6)}^{2} + 6 (- 6) - 7$

Step 3

Simplify ${(- 6)}^{2} + 6 (- 6) - 7$ .

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Step 3.1

Remove parentheses.

${(- 6)}^{2} + 6 (- 6) - 7$

Step 3.2

Simplify each term.

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Step 3.2.1

Raise $- 6$ to the power of $2$ .

$36 + 6 (- 6) - 7$

Step 3.2.2

Multiply $6$ by $- 6$ .

$36 - 36 - 7$

Step 3.3

Simplify by subtracting numbers.

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Step 3.3.1

Subtract $36$ from $36$ .

$0 - 7$

Step 3.3.2

Subtract $7$ from $0$ .

$- 7$