Algebra Examples

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

Step 1

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

$y = f (2 x)$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = f \cdot (2 x)$

Step 2.2

Rewrite using the commutative property of multiplication.

$y = 2 f x$

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

Multiply $2 f$ by $0$ .

$y = 2 f \cdot 0$

Step 4.2

Remove parentheses.

$y = 2 f (0)$

Step 4.3

Multiply $2 f (0)$ .

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Step 4.3.1

Multiply $0$ by $2$ .

$y = 0 f$

Step 4.3.2

Multiply $0$ by $f$ .

$y = 0$

Step 4.4

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

$(0, 0, 1)$

Step 5

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

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Step 5.1

Multiply $2 f$ by $1$ .

$y = 2 f \cdot 1$

Step 5.2

Remove parentheses.

$y = 2 f (1)$

Step 5.3

Multiply $2$ by $1$ .

$y = 2 f$

Step 5.4

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

$(1, 2 f, 2)$

Step 6

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

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Step 6.1

Multiply $2 f$ by $2$ .

$y = 2 f \cdot 2$

Step 6.2

Remove parentheses.

$y = 2 f (2)$

Step 6.3

Multiply $2$ by $2$ .

$y = 4 f$

Step 6.4

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

$(2, 4 f, 3)$

Step 7

These are three possible solutions to the equation.

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