Algebra Examples

$g (x) = 2 f (\frac{1}{2} x)$

Step 1

Write $g (x) = 2 f (\frac{1}{2} x)$ as an equation.

$y = 2 f (\frac{1}{2} x)$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = 2 f (\frac{1}{2}) \cdot x$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $2 f$ .

$y = 2 (f) \frac{1}{2} \cdot x$

Step 2.2.2

Cancel the common factor.

$y = 2 f \frac{1}{2} \cdot x$

Step 2.2.3

Rewrite the expression.

$y = f \cdot x$

$y = f x$

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

Remove parentheses.

$y = f (0)$

Step 4.2

Multiply $f$ by $0$ .

$y = 0$

Step 4.3

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

Remove parentheses.

$y = f (1)$

Step 5.2

Multiply $f$ by $1$ .

$y = f$

Step 5.3

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

$(1, f, 2)$

Step 6

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

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Step 6.1

Remove parentheses.

$y = f (2)$

Step 6.2

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

$y = 2 f$

Step 6.3

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

$(2, 2 f, 3)$

Step 7

These are three possible solutions to the equation.

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