Calculus Examples

$f (x) = 12 {(x - 1)}^{\frac{2}{3}} - 4 {(x - 1)}^{2}$

Step 1

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

$(- \infty, \infty)$

${x | x \in ℝ}$

Step 2

The range is the set of all valid $y$ values. Use the graph to find the range.

$(- \infty, \infty)$

${y | y \in ℝ}$

Step 3

Determine the domain and range.

Domain: $(- \infty, \infty), {x | x \in ℝ}$

Range: $(- \infty, \infty), {y | y \in ℝ}$