Algebra Examples

$f (x) = 4 x - 3$ and $g (x) = \frac{1}{4} x + 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{1}{4} x + 3)$ by substituting in the value of $g$ into $f$ .

$f (\frac{1}{4} x + 3) = 4 (\frac{1}{4} x + 3) - 3$

Step 3

Simplify each term.

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Step 3.1

Combine $\frac{1}{4}$ and $x$ .

$f (\frac{1}{4} x + 3) = 4 (\frac{x}{4} + 3) - 3$

Step 3.2

Apply the distributive property.

$f (\frac{1}{4} x + 3) = 4 (\frac{x}{4}) + 4 \cdot 3 - 3$

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Cancel the common factor.

$f (\frac{1}{4} x + 3) = 4 (\frac{x}{4}) + 4 \cdot 3 - 3$

Step 3.3.2

Rewrite the expression.

$f (\frac{1}{4} x + 3) = x + 4 \cdot 3 - 3$

Step 3.4

Multiply $4$ by $3$ .

$f (\frac{1}{4} x + 3) = x + 12 - 3$

Step 4

Subtract $3$ from $12$ .

$f (\frac{1}{4} x + 3) = x + 9$