Question

question 4
consider the function: $g(x) = \sqrt3{x + 4}$
which ordered pair lies on the inverse of the function?
\bigcirc (-1,-2)
\bigcirc (-4,-1)
\bigcirc (0,-4)
\bigcirc (3,1)

Explanation:

Step1: Find the inverse of \( g(x) \)

Let \( y = \sqrt[3]{x + 4} \). To find the inverse, we first swap \( x \) and \( y \): \( x = \sqrt[3]{y + 4} \). Then we solve for \( y \). Cube both sides: \( x^3 = y + 4 \), so \( y = x^3 - 4 \). Thus, the inverse function \( g^{-1}(x)=x^3 - 4 \).

Step2: Test each ordered pair

• For \((-1, -2)\): Plug \( x=-1 \) into \( g^{-1}(x) \), we get \( (-1)^3 - 4=-1 - 4=-5

eq - 2 \).

• For \((-4, -1)\): Plug \( x = - 4 \) into \( g^{-1}(x) \), we get \( (-4)^3-4=-64 - 4=-68

eq - 1 \).

• For \((0, -4)\): Plug \( x = 0 \) into \( g^{-1}(x) \), we get \( 0^3-4=-4 \). So when \( x = 0 \), \( y=-4 \), so \((0, - 4)\) lies on the inverse function.
• For \((3,1)\): Plug \( x = 3 \) into \( g^{-1}(x) \), we get \( 3^3-4 = 27-4 = 23

eq1 \).

Answer:

\((0, - 4)\)