Algebra Examples

$f (x) = 2 x - 7$ , $g (x) = \frac{1}{2} (x + 7)$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{1}{2} \cdot (x + 7))$ by substituting in the value of $g$ into $f$ .

$f (\frac{1}{2} \cdot (x + 7)) = 2 (\frac{1}{2} \cdot (x + 7)) - 7$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (\frac{1}{2} \cdot (x + 7)) = 2 (\frac{1}{2} x + \frac{1}{2} \cdot 7) - 7$

Step 3.2

Combine $\frac{1}{2}$ and $x$ .

$f (\frac{1}{2} \cdot (x + 7)) = 2 (\frac{x}{2} + \frac{1}{2} \cdot 7) - 7$

Step 3.3

Combine $\frac{1}{2}$ and $7$ .

$f (\frac{1}{2} \cdot (x + 7)) = 2 (\frac{x}{2} + \frac{7}{2}) - 7$

Step 3.4

Apply the distributive property.

$f (\frac{1}{2} \cdot (x + 7)) = 2 (\frac{x}{2}) + 2 (\frac{7}{2}) - 7$

Step 3.5

Cancel the common factor of $2$ .

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Step 3.5.1

Cancel the common factor.

$f (\frac{1}{2} \cdot (x + 7)) = 2 (\frac{x}{2}) + 2 (\frac{7}{2}) - 7$

Step 3.5.2

Rewrite the expression.

$f (\frac{1}{2} \cdot (x + 7)) = x + 2 (\frac{7}{2}) - 7$

Step 3.6

Cancel the common factor of $2$ .

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Step 3.6.1

Cancel the common factor.

$f (\frac{1}{2} \cdot (x + 7)) = x + 2 (\frac{7}{2}) - 7$

Step 3.6.2

Rewrite the expression.

$f (\frac{1}{2} \cdot (x + 7)) = x + 7 - 7$

Step 4

Combine the opposite terms in $x + 7 - 7$ .

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Step 4.1

Subtract $7$ from $7$ .

$f (\frac{1}{2} \cdot (x + 7)) = x + 0$

Step 4.2

Add $x$ and $0$ .

$f (\frac{1}{2} \cdot (x + 7)) = x$