Algebra Examples

$f (x) = 4 x^{3} - 10$ $g (x) = \frac{3 x - 4}{2}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (4 x^{3} - 10)$ by substituting in the value of $f$ into $g$ .

$g (4 x^{3} - 10) = \frac{3 (4 x^{3} - 10) - 4}{2}$

Step 3

Simplify the numerator.

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Step 3.1

Apply the distributive property.

$g (4 x^{3} - 10) = \frac{3 (4 x^{3}) + 3 \cdot - 10 - 4}{2}$

Step 3.2

Multiply $4$ by $3$ .

$g (4 x^{3} - 10) = \frac{12 x^{3} + 3 \cdot - 10 - 4}{2}$

Step 3.3

Multiply $3$ by $- 10$ .

$g (4 x^{3} - 10) = \frac{12 x^{3} - 30 - 4}{2}$

Step 3.4

Subtract $4$ from $- 30$ .

$g (4 x^{3} - 10) = \frac{12 x^{3} - 34}{2}$

Step 3.5

Factor $2$ out of $12 x^{3} - 34$ .

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Step 3.5.1

Factor $2$ out of $12 x^{3}$ .

$g (4 x^{3} - 10) = \frac{2 (6 x^{3}) - 34}{2}$

Step 3.5.2

Factor $2$ out of $- 34$ .

$g (4 x^{3} - 10) = \frac{2 (6 x^{3}) + 2 (- 17)}{2}$

Step 3.5.3

Factor $2$ out of $2 (6 x^{3}) + 2 (- 17)$ .

$g (4 x^{3} - 10) = \frac{2 (6 x^{3} - 17)}{2}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

$g (4 x^{3} - 10) = \frac{2 (6 x^{3} - 17)}{2}$

Step 4.2

Divide $6 x^{3} - 17$ by $1$ .

$g (4 x^{3} - 10) = 6 x^{3} - 17$