Calculus Examples

$f (x) = \frac{x}{10} + 3$ , $g (x) = 8 x - 1$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{x}{10} + 3)$ by substituting in the value of $f$ into $g$ .

$g (\frac{x}{10} + 3) = 8 (\frac{x}{10} + 3) - 1$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (\frac{x}{10} + 3) = 8 (\frac{x}{10}) + 8 \cdot 3 - 1$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $8$ .

$g (\frac{x}{10} + 3) = 2 (4) (\frac{x}{10}) + 8 \cdot 3 - 1$

Step 3.2.2

Factor $2$ out of $10$ .

$g (\frac{x}{10} + 3) = 2 \cdot (4 (\frac{x}{2 \cdot 5})) + 8 \cdot 3 - 1$

Step 3.2.3

Cancel the common factor.

$g (\frac{x}{10} + 3) = 2 \cdot (4 (\frac{x}{2 \cdot 5})) + 8 \cdot 3 - 1$

Step 3.2.4

Rewrite the expression.

$g (\frac{x}{10} + 3) = 4 (\frac{x}{5}) + 8 \cdot 3 - 1$

Step 3.3

Combine $4$ and $\frac{x}{5}$ .

$g (\frac{x}{10} + 3) = \frac{4 x}{5} + 8 \cdot 3 - 1$

Step 3.4

Multiply $8$ by $3$ .

$g (\frac{x}{10} + 3) = \frac{4 x}{5} + 24 - 1$

Step 4

Subtract $1$ from $24$ .

$g (\frac{x}{10} + 3) = \frac{4 x}{5} + 23$