Algebra Examples

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{x}{2} - 1)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

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

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

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

Step 3.3

Multiply $2$ by $- 1$ .

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

Step 4

Combine the opposite terms in $x - 2 + 2$ .

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Step 4.1

Add $- 2$ and $2$ .

$f (\frac{x}{2} - 1) = x + 0$

Step 4.2

Add $x$ and $0$ .

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