Calculus Examples

$f (x) = \frac{x}{10} + 7$ , $g (x) = 4 x - 1$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (4 x - 1)$ by substituting in the value of $g$ into $f$ .

$f (4 x - 1) = \frac{4 x - 1}{10} + 7$

Step 3

To write $7$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$f (4 x - 1) = \frac{4 x - 1}{10} + 7 \cdot \frac{10}{10}$

Step 4

Simplify terms.

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Step 4.1

Combine $7$ and $\frac{10}{10}$ .

$f (4 x - 1) = \frac{4 x - 1}{10} + \frac{7 \cdot 10}{10}$

Step 4.2

Combine the numerators over the common denominator.

$f (4 x - 1) = \frac{4 x - 1 + 7 \cdot 10}{10}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $7$ by $10$ .

$f (4 x - 1) = \frac{4 x - 1 + 70}{10}$

Step 5.2

Add $- 1$ and $70$ .

$f (4 x - 1) = \frac{4 x + 69}{10}$