Algebra Examples

$f (x) = \frac{x}{4} - 3$ , $g (x) = 4 x^{2} + 2 x - 4$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (4 x^{2} + 2 x - 4)$ by substituting in the value of $g$ into $f$ .

$f (4 x^{2} + 2 x - 4) = \frac{4 x^{2} + 2 x - 4}{4} - 3$

Step 3

Cancel the common factor of $4 x^{2} + 2 x - 4$ and $4$ .

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Step 3.1

Factor $2$ out of $4 x^{2}$ .

$f (4 x^{2} + 2 x - 4) = \frac{2 (2 x^{2}) + 2 x - 4}{4} - 3$

Step 3.2

Factor $2$ out of $2 x$ .

$f (4 x^{2} + 2 x - 4) = \frac{2 (2 x^{2}) + 2 (x) - 4}{4} - 3$

Step 3.3

Factor $2$ out of $2 (2 x^{2}) + 2 (x)$ .

$f (4 x^{2} + 2 x - 4) = \frac{2 (2 x^{2} + x) - 4}{4} - 3$

Step 3.4

Factor $2$ out of $- 4$ .

$f (4 x^{2} + 2 x - 4) = \frac{2 (2 x^{2} + x) + 2 (- 2)}{4} - 3$

Step 3.5

Factor $2$ out of $2 (2 x^{2} + x) + 2 (- 2)$ .

$f (4 x^{2} + 2 x - 4) = \frac{2 (2 x^{2} + x - 2)}{4} - 3$

Step 3.6

Cancel the common factors.

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Step 3.6.1

Factor $2$ out of $4$ .

$f (4 x^{2} + 2 x - 4) = \frac{2 (2 x^{2} + x - 2)}{2 (2)} - 3$

Step 3.6.2

Cancel the common factor.

$f (4 x^{2} + 2 x - 4) = \frac{2 (2 x^{2} + x - 2)}{2 \cdot 2} - 3$

Step 3.6.3

Rewrite the expression.

$f (4 x^{2} + 2 x - 4) = \frac{2 x^{2} + x - 2}{2} - 3$

Step 4

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$f (4 x^{2} + 2 x - 4) = \frac{2 x^{2} + x - 2}{2} - 3 \cdot \frac{2}{2}$

Step 5

Simplify terms.

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Step 5.1

Combine $- 3$ and $\frac{2}{2}$ .

$f (4 x^{2} + 2 x - 4) = \frac{2 x^{2} + x - 2}{2} + \frac{- 3 \cdot 2}{2}$

Step 5.2

Combine the numerators over the common denominator.

$f (4 x^{2} + 2 x - 4) = \frac{2 x^{2} + x - 2 - 3 \cdot 2}{2}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 3$ by $2$ .

$f (4 x^{2} + 2 x - 4) = \frac{2 x^{2} + x - 2 - 6}{2}$

Step 6.2

Subtract $6$ from $- 2$ .

$f (4 x^{2} + 2 x - 4) = \frac{2 x^{2} + x - 8}{2}$