Algebra Examples

$g (x) = f (x - 1) - 2$

Step 1

Write $g (x) = f (x - 1) - 2$ as an equation.

$y = f (x - 1) - 2$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$y = f x + f \cdot - 1 - 2$

Step 2.2

Move $- 1$ to the left of $f$ .

$y = f x - 1 \cdot f - 2$

Step 2.3

Rewrite $- 1 f$ as $- f$ .

$y = f x - f - 2$

Step 3

Choose any values for $x$ and $y$ that are in the domain to plug into the equation.

Step 4

Choose $0$ to substitute in for $x$ and $1$ to substitute for $z$ .

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Step 4.1

Remove parentheses.

$y = f (0) - f - 2$

Step 4.2

Simplify $f (0) - f - 2$ .

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Step 4.2.1

Multiply $f$ by $0$ .

$y = 0 - f - 2$

Step 4.2.2

Subtract $f$ from $0$ .

$y = - f - 2$

Step 4.3

Use the $x$ , $y$ , and $z$ values to form the ordered pair.

$(0, - f - 2, 1)$

Step 5

Choose $1$ to substitute in for $x$ and $2$ to substitute for $z$ .

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Step 5.1

Remove parentheses.

$y = f (1) - f - 2$

Step 5.2

Simplify $f (1) - f - 2$ .

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Step 5.2.1

Multiply $f$ by $1$ .

$y = f - f - 2$

Step 5.2.2

Subtract $f$ from $f$ .

$y = 0 - 2$

Step 5.2.3

Subtract $2$ from $0$ .

$y = - 2$

Step 5.3

Use the $x$ , $y$ , and $z$ values to form the ordered pair.

$(1, - 2, 2)$

Step 6

Choose $2$ to substitute in for $x$ and $3$ to substitute for $z$ .

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Step 6.1

Remove parentheses.

$y = f (2) - f - 2$

Step 6.2

Simplify $f (2) - f - 2$ .

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Step 6.2.1

Move $2$ to the left of $f$ .

$y = 2 f - f - 2$

Step 6.2.2

Subtract $f$ from $2 f$ .

$y = f - 2$

Step 6.3

Use the $x$ , $y$ , and $z$ values to form the ordered pair.

$(2, f - 2, 3)$

Step 7

These are three possible solutions to the equation.

$(0, - f - 2, 1), (1, - 2, 2), (2, f - 2, 3)$