Algebra Examples

$f (x + 3)$

Step 1

Write $f (x + 3)$ as a function.

$f (x) = f (x + 3)$

Step 2

Write $f (x) = f (x + 3)$ as an equation.

$y = f (x + 3)$

Step 3

Simplify $f (x + 3)$ .

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Step 3.1

Apply the distributive property.

$y = f x + f \cdot 3$

Step 3.2

Move $3$ to the left of $f$ .

$y = f x + 3 f$

Step 4

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

Step 5

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

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Step 5.1

Remove parentheses.

$y = f (0) + 3 f$

Step 5.2

Simplify $f (0) + 3 f$ .

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Step 5.2.1

Multiply $f$ by $0$ .

$y = 0 + 3 f$

Step 5.2.2

Add $0$ and $3 f$ .

$y = 3 f$

Step 5.3

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

$(0, 3 f, 1)$

Step 6

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

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Step 6.1

Remove parentheses.

$y = f (1) + 3 f$

Step 6.2

Simplify $f (1) + 3 f$ .

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Step 6.2.1

Multiply $f$ by $1$ .

$y = f + 3 f$

Step 6.2.2

Add $f$ and $3 f$ .

$y = 4 f$

Step 6.3

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

$(1, 4 f, 2)$

Step 7

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

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Step 7.1

Remove parentheses.

$y = f (2) + 3 f$

Step 7.2

Simplify $f (2) + 3 f$ .

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Step 7.2.1

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

$y = 2 f + 3 f$

Step 7.2.2

Add $2 f$ and $3 f$ .

$y = 5 f$

Step 7.3

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

$(2, 5 f, 3)$

Step 8

These are three possible solutions to the equation.

$(0, 3 f, 1), (1, 4 f, 2), (2, 5 f, 3)$