Algebra Examples

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (2 x - 3)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify the numerator.

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Step 3.1

Subtract $3$ from $- 3$ .

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

Step 3.2

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

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Step 3.2.1

Factor $2$ out of $2 x$ .

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

Step 3.2.2

Factor $2$ out of $- 6$ .

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

Step 3.2.3

Factor $2$ out of $2 x + 2 \cdot - 3$ .

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

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Divide $x - 3$ by $1$ .

$f (2 x - 3) = x - 3$