Question

solve $y = f(x)$ for $x$. then find the input when the output is $-3$.
$f(x) = (x + 2)^3 - 3$
$x = \square$
the input is $\square$ when the output is $-3$.

Explanation:

Step1: Replace f(x) with y

$y = (x+2)^3 - 3$

Step2: Isolate the cubic term

$y + 3 = (x+2)^3$

Step3: Take cube root of both sides

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

Step4: Solve for x

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

Step5: Substitute y = -3

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

Step6: Simplify the expression

$x = \sqrt[3]{0} - 2 = 0 - 2 = -2$

Answer:

$x = \sqrt[3]{y + 3} - 2$
The input is $-2$ when the output is $-3$.