Trigonometry Examples

$f (x) = - \frac{7}{2} x - 3$ , $g (x) = \frac{- 2 x + 6}{7}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{- 2 x + 6}{7})$ by substituting in the value of $g$ into $f$ .

$f (\frac{- 2 x + 6}{7}) = - \frac{7}{2} \cdot \frac{- 2 x + 6}{7} - 3$

Step 3

Simplify each term.

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Step 3.1

Factor $2$ out of $- 2 x + 6$ .

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Step 3.1.1

Factor $2$ out of $- 2 x$ .

$f (\frac{- 2 x + 6}{7}) = - \frac{7}{2} \cdot \frac{2 (- x) + 6}{7} - 3$

Step 3.1.2

Factor $2$ out of $6$ .

$f (\frac{- 2 x + 6}{7}) = - \frac{7}{2} \cdot \frac{2 (- x) + 2 (3)}{7} - 3$

Step 3.1.3

Factor $2$ out of $2 (- x) + 2 (3)$ .

$f (\frac{- 2 x + 6}{7}) = - \frac{7}{2} \cdot \frac{2 (- x + 3)}{7} - 3$

Step 3.2

Cancel the common factor of $7$ .

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Step 3.2.1

Move the leading negative in $- \frac{7}{2}$ into the numerator.

$f (\frac{- 2 x + 6}{7}) = \frac{- 7}{2} \cdot \frac{2 (- x + 3)}{7} - 3$

Step 3.2.2

Factor $7$ out of $- 7$ .

$f (\frac{- 2 x + 6}{7}) = \frac{7 (- 1)}{2} \cdot \frac{2 (- x + 3)}{7} - 3$

Step 3.2.3

Cancel the common factor.

$f (\frac{- 2 x + 6}{7}) = \frac{7 \cdot - 1}{2} \cdot \frac{2 (- x + 3)}{7} - 3$

Step 3.2.4

Rewrite the expression.

$f (\frac{- 2 x + 6}{7}) = \frac{- 1}{2} \cdot (2 (- x + 3)) - 3$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Cancel the common factor.

$f (\frac{- 2 x + 6}{7}) = \frac{- 1}{2} \cdot (2 (- x + 3)) - 3$

Step 3.3.2

Rewrite the expression.

$f (\frac{- 2 x + 6}{7}) = - 1 \cdot (- x + 3) - 3$

Step 3.4

Apply the distributive property.

$f (\frac{- 2 x + 6}{7}) = - 1 (- x) - 1 \cdot 3 - 3$

Step 3.5

Multiply $- 1 (- x)$ .

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Step 3.5.1

Multiply $- 1$ by $- 1$ .

$f (\frac{- 2 x + 6}{7}) = 1 x - 1 \cdot 3 - 3$

Step 3.5.2

Multiply $x$ by $1$ .

$f (\frac{- 2 x + 6}{7}) = x - 1 \cdot 3 - 3$

Step 3.6

Multiply $- 1$ by $3$ .

$f (\frac{- 2 x + 6}{7}) = x - 3 - 3$

Step 4

Subtract $3$ from $- 3$ .

$f (\frac{- 2 x + 6}{7}) = x - 6$