Algebra Examples

$x = {(y + 1)}^{3} - 2$

Step 1

Rewrite the equation as ${(y + 1)}^{3} - 2 = x$ .

${(y + 1)}^{3} - 2 = x$

Step 2

Add $2$ to both sides of the equation.

${(y + 1)}^{3} = x + 2$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y + 1 = \sqrt[3]{x + 2}$

Step 4

Subtract $1$ from both sides of the equation.

$y = \sqrt[3]{x + 2} - 1$

Step 5

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.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 6

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

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Step 7

Determine the domain and range.

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

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

Step 8