Algebra Examples

$f (x) = 3 x - 3$ , $g (x) = \frac{1}{3} x + 1$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{1}{3} x + 1)$ by substituting in the value of $g$ into $f$ .

$f (\frac{1}{3} x + 1) = 3 (\frac{1}{3} x + 1) - 3$

Step 3

Simplify each term.

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Step 3.1

Combine $\frac{1}{3}$ and $x$ .

$f (\frac{1}{3} x + 1) = 3 (\frac{x}{3} + 1) - 3$

Step 3.2

Apply the distributive property.

$f (\frac{1}{3} x + 1) = 3 (\frac{x}{3}) + 3 \cdot 1 - 3$

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Cancel the common factor.

$f (\frac{1}{3} x + 1) = 3 (\frac{x}{3}) + 3 \cdot 1 - 3$

Step 3.3.2

Rewrite the expression.

$f (\frac{1}{3} x + 1) = x + 3 \cdot 1 - 3$

Step 3.4

Multiply $3$ by $1$ .

$f (\frac{1}{3} x + 1) = x + 3 - 3$

Step 4

Combine the opposite terms in $x + 3 - 3$ .

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Step 4.1

Subtract $3$ from $3$ .

$f (\frac{1}{3} x + 1) = x + 0$

Step 4.2

Add $x$ and $0$ .

$f (\frac{1}{3} x + 1) = x$