Algebra Examples

$f (x) = 6 x - 5$ $g (x) = \frac{1}{6} (x + 5)$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{1}{6} \cdot (x + 5))$ by substituting in the value of $g$ into $f$ .

$f (\frac{1}{6} \cdot (x + 5)) = 6 (\frac{1}{6} \cdot (x + 5)) - 5$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (\frac{1}{6} \cdot (x + 5)) = 6 (\frac{1}{6} x + \frac{1}{6} \cdot 5) - 5$

Step 3.2

Combine $\frac{1}{6}$ and $x$ .

$f (\frac{1}{6} \cdot (x + 5)) = 6 (\frac{x}{6} + \frac{1}{6} \cdot 5) - 5$

Step 3.3

Combine $\frac{1}{6}$ and $5$ .

$f (\frac{1}{6} \cdot (x + 5)) = 6 (\frac{x}{6} + \frac{5}{6}) - 5$

Step 3.4

Apply the distributive property.

$f (\frac{1}{6} \cdot (x + 5)) = 6 (\frac{x}{6}) + 6 (\frac{5}{6}) - 5$

Step 3.5

Cancel the common factor of $6$ .

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Step 3.5.1

Cancel the common factor.

$f (\frac{1}{6} \cdot (x + 5)) = 6 (\frac{x}{6}) + 6 (\frac{5}{6}) - 5$

Step 3.5.2

Rewrite the expression.

$f (\frac{1}{6} \cdot (x + 5)) = x + 6 (\frac{5}{6}) - 5$

Step 3.6

Cancel the common factor of $6$ .

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Step 3.6.1

Cancel the common factor.

$f (\frac{1}{6} \cdot (x + 5)) = x + 6 (\frac{5}{6}) - 5$

Step 3.6.2

Rewrite the expression.

$f (\frac{1}{6} \cdot (x + 5)) = x + 5 - 5$

Step 4

Combine the opposite terms in $x + 5 - 5$ .

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Step 4.1

Subtract $5$ from $5$ .

$f (\frac{1}{6} \cdot (x + 5)) = x + 0$

Step 4.2

Add $x$ and $0$ .

$f (\frac{1}{6} \cdot (x + 5)) = x$