Algebra Examples

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

$g (\frac{7}{2} x) = - \frac{2}{7} \cdot (\frac{7}{2} x)$

Step 3

Combine $\frac{7}{2}$ and $x$ .

$g (\frac{7}{2} x) = - \frac{2}{7} \cdot \frac{7 x}{2}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

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

$g (\frac{7}{2} x) = \frac{- 2}{7} \cdot \frac{7 x}{2}$

Step 4.2

Factor $2$ out of $- 2$ .

$g (\frac{7}{2} x) = \frac{2 (- 1)}{7} \cdot \frac{7 x}{2}$

Step 4.3

Cancel the common factor.

$g (\frac{7}{2} x) = \frac{2 \cdot - 1}{7} \cdot \frac{7 x}{2}$

Step 4.4

Rewrite the expression.

$g (\frac{7}{2} x) = \frac{- 1}{7} \cdot (7 x)$

Step 5

Cancel the common factor of $7$ .

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Step 5.1

Factor $7$ out of $7 x$ .

$g (\frac{7}{2} x) = \frac{- 1}{7} \cdot (7 (x))$

Step 5.2

Cancel the common factor.

$g (\frac{7}{2} x) = \frac{- 1}{7} \cdot (7 x)$

Step 5.3

Rewrite the expression.

$g (\frac{7}{2} x) = - 1 \cdot x$

Step 6

Rewrite $- 1 x$ as $- x$ .

$g (\frac{7}{2} x) = - x$