Question

consider the function : $g(x) = -(x - 3)^3 + 2$
which ordered pair lies on the inverse of the function?
$\bigcirc$ $(-2, 123)$
$\bigcirc$ $(-3, 4)$
$\bigcirc$ $(62, -3)$
$\bigcirc$ $(9, 25)$

Explanation:

Step1: Recall inverse pair property

If $(a,b)$ is on $g(x)$, then $(b,a)$ is on $g^{-1}(x)$.

Step2: Test option D (0,25)

Check if $(25,0)$ is on $g(x)$:

$$g(25) = -(25-3)^3 - 2 = -(22)^3 - 2 = -10648 - 2 = -10650 eq 0$$

Step3: Test option C (62,-3)

Check if $(-3,62)$ is on $g(x)$:

$$g(-3) = -(-3-3)^3 - 2 = -(-6)^3 - 2 = -(-216) - 2 = 216 - 2 = 214 eq 62$$

Step4: Test option B (-3,4)

Check if $(4,-3)$ is on $g(x)$:
$$g(4) = -(4-3)^3 - 2 = -(1)^3 - 2 = -1 - 2 = -3$$
This matches the y-value of -3.

Step5: Verify option A (optional)

Check if $(123,-2)$ is on $g(x)$:

$$g(123) = -(123-3)^3 - 2 = -(120)^3 - 2 = -1728000 - 2 = -1728002 eq -2$$

Answer:

B. (-3,4)