Precalculus Examples

$f (x) = 4^{x} - 8$ and $g (x) = 5 x + 6$ ; find $(f - g) (x)$

Step 1

Evaluate $f - g$ .

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Step 1.1

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

$(4^{x} - 8) - (5 x + 6)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$4^{x} - 8 - (5 x) - 1 \cdot 6$

Step 1.2.2

Multiply $5$ by $- 1$ .

$4^{x} - 8 - 5 x - 1 \cdot 6$

Step 1.2.3

Multiply $- 1$ by $6$ .

$4^{x} - 8 - 5 x - 6$

Step 1.3

Simplify the expression.

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Step 1.3.1

Subtract $6$ from $- 8$ .

$4^{x} - 5 x - 14$

Step 1.3.2

Reorder $4^{x}$ and $- 5 x$ .

$- 5 x + 4^{x} - 14$

Step 2

Evaluate $f - g$ at $x$ .

$- 5 x + 4^{x} - 14$

Step 3

Remove parentheses.

$- 5 x + 4^{x} - 14$