Algebra Examples

$f (x) = 3 x + 5$ and $g (x) = 5 x - 1$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (5 x - 1)$ by substituting in the value of $g$ into $f$ .

$f (5 x - 1) = 3 (5 x - 1) + 5$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (5 x - 1) = 3 (5 x) + 3 \cdot - 1 + 5$

Step 3.2

Multiply $5$ by $3$ .

$f (5 x - 1) = 15 x + 3 \cdot - 1 + 5$

Step 3.3

Multiply $3$ by $- 1$ .

$f (5 x - 1) = 15 x - 3 + 5$

Step 4

Add $- 3$ and $5$ .

$f (5 x - 1) = 15 x + 2$